Unsurprisingly, in modern times, the Catholic Church's position on slavery is one of unambiguous staunch opposition:
Catechism of the Catholic Church 2414
2414 The seventh commandment forbids acts or enterprises that for any reason - selfish or ideological, commercial, or totalitarian - lead to the enslavement of human beings, to their being bought, sold and exchanged like merchandise, in disregard for their personal dignity. It is a sin against the dignity of persons and their fundamental rights to reduce them by violence to their productive value or to a source of profit. St. Paul directed a Christian master to treat his Christian slave "no longer as a slave but more than a slave, as a beloved brother... both in the flesh and in the Lord."
Vatican 2 - Gaudium Et Spes (1965 AD)
27 Furthermore, whatever is opposed to life itself, such as any type of murder, genocide, abortion, euthanasia or wilful self-destruction, whatever violates the integrity of the human person, such as mutilation, torments inflicted on body or mind, attempts to coerce the will itself; whatever insults human dignity, such as subhuman living conditions, arbitrary imprisonment, deportation, slavery, prostitution, the selling of women and children; as well as disgraceful working conditions, where men are treated as mere tools for profit, rather than as free and responsible persons; all these things and others of their like are infamies indeed. They poison human society, but they do more harm to those who practice them than those who suffer from the injury. Moreover, they are supreme dishonor to the Creator.
29 Human institutions, both private and public, must labor to minister to the dignity and purpose of man. At the same time let them put up a stubborn fight against any kind of slavery, whether social or political, and safeguard the basic rights of man under every political system.
Aside from contemporary examples, of which there are dozens, it is also true that historically, one can find Papal pronouncements against slavery in various contexts.
For instance:
Pope Eugene IV - Sicut Dudum (1435 AD)
4 And no less do We order and command all and each of the faithful of each sex, within the space of fifteen days of the publication of these letters in the place where they live, that they restore to their earlier liberty all and each person of either sex who were once residents of said Canary Islands, and made captives since the time of their capture, and who have been made subject to slavery.
These people are to be totally and perpetually free, and are to be let go without the exaction or reception of money. We will that like sentence of excommunication be incurred by one and all who attempt to capture, sell, or subject to slavery, baptized residents of the Canary Islands, or those who are freely seeking Baptism, from which excommunication cannot be absolved except as was stated above.
The above applies to baptized or would-be baptized natives from the Canary Islands, and forbids their enslavement.
A later Bull by Pope Paul III forbade enslavement of any Indians that Christians would encounter in the New World - baptized or unbaptized:
Pope Paul III - Sublimis Deus (1537 AD)
Desiring to provide ample remedy for these evils, We define and declare by these Our letters, or by any translation thereof signed by any notary public and sealed with the seal of any ecclesiastical dignitary, to which the same credit shall be given as to the originals, that, notwithstanding whatever may have been or may be said to the contrary, the said Indians and all other people who may later be discovered by Christians, are by no means to be deprived of their liberty or the possession of their property, even though they be outside the faith of Jesus Christ; and that they may and should, freely and legitimately, enjoy their liberty and the possession of their property; nor should they be in any way enslaved; should the contrary happen, it shall be null and have no effect.
These anti-slavery citations could be multiplied, especially after the 19th century.
So, clearly there is historical precedent proving that the Catholic Church, at times, forbade slavery. And, at present, they unequivocally forbid it, and use moral language to make it very clear that it is sinful, regardless of the circumstances.
There are also historical examples of the Catholic Church allowing, or even seemingly prescribing slavery.
One of these is highly significant, because it's part of the Third Lateran Council (1179 AD), which is ecumenical:
Third Lateran Council (1179 AD) - Canons 24, 27
24 Cruel avarice has so seized the hearts of some that though they glory in the name of Christians they provide the Saracens with arms and wood for helmets, and become their equals or even their superiors in wickedness and supply them with arms and necessaries to attack Christians. There are even some who for gain act as captains or pilots in galleys or Saracen pirate vessels. Therefore we declare that such persons should be cut off from the communion of the church and be excommunicated for their wickedness, that catholic princes and civil magistrates should confiscate their possessions, and that if they are captured they should become the slaves of their captors.
27 As long as such people persist in their wickedness, let all who are bound to them by any pact know that they are free from all obligations of loyalty, homage or any obedience. On these and on all the faithful we enjoin, for the remission of sins, that they oppose this scourge with all their might and by arms protect the christian people against them. Their goods are to be confiscated and princes free to subject them to slavery.
The above prescribes slavery for those who aid the Saracens (Arabs), and also allows the enslavement of those who belonged to groups of marauders that attacked and raided Christian communities. According to Vatican 2 - also an ecumenical council - because the above imposition resulted in a situation where "men are treated as mere tools for profit, rather than as free and responsible persons", the above "insults human dignity", and does "supreme dishonor to the Creator".
Next, a significant figure in this discussion is Pope Nicholas V (1397-1455 AD), who issued two Papal Bulls granting permission for the wholesale enslavement of West African peoples under Portuguese rule:
Pope Nicholas V - Dum Diversas (1452 AD)
We grant to you full and free power, through the Apostolic authority by this edict, to invade, conquer, fight, subjugate the Saracens and pagans, and other infidels and other enemies of Christ, and wherever established their Kingdoms, Duchies, Royal Palaces, Principalities and other dominions, lands, places, estates, camps and any other possessions, mobile and immobile goods found in all these places and held in whatever name, and held and possessed by the same Saracens, Pagans, infidels, and the enemies of Christ, also realms, duchies, royal palaces, principalities and other dominions, lands, places, estates, camps, possessions of the king or prince or of the kings or princes, and to lead their persons in perpetual servitude, and to apply and appropriate realms, duchies, royal palaces, principalities and other dominions, possessions and goods of this kind to you and your use and your successors the Kings of Portugal.
Pope Nicholas V - Romanus Pontifex (1455 AD)
We [therefore] weighing all and singular the premises with due meditation, and noting that since we had formerly by other letters of ours granted among other things free and ample faculty to the aforesaid King Alfonso — to invade, search out, capture, vanquish, and subdue all Saracens and pagans whatsoever, and other enemies of Christ wheresoever placed, and the kingdoms, dukedoms, principalities, dominions, possessions, and all movable and immovable goods whatsoever held and possessed by them and to reduce their persons to perpetual slavery, and to apply and appropriate to himself and his successors the kingdoms, dukedoms, counties, principalities, dominions, possessions, and goods, and to convert them to his and their use and profit
The phrase "perpetual servitude/slavery" can arguably be seen in a feudal sense - i.e., these conquered peoples were forever to be subject to the Portuguese, rather than individually enslaved. However, both texts mention "their persons", which seems to grant permission for the Portuguese to have autonomy over individuals themselves.
Adding to this, before its enslavement passage, Dum Diversas already grants permission to "conquer, fight, (and) subjugate" the peoples in question. If "lead their persons into perpetual servitude" referred to merely subjugation of the people group as a whole, it would then be redundant. Likewise, Romanus Pontifex, prior to its enslavement passage, grants permission to capture "all movable and immovable goods whatsoever held and possessed by them". That doesn't sound like vassalage, it sounds like slavery.
Further, Pope Francis has recognized that Dum Diversas tolerated slavery, and used it as an example of contextualized doctrine that isn't necessarily valid for all places and all time:
Pope Francis - Dubia of Two Cardinals and Response of the Holy Father (September 25, 2023)
(f) It is true, on the other hand, that the Magisterium is not superior to the Word of God, but it is also true that the texts of Scripture and the testimonies of Tradition require an interpretation that allows their perennial substance to be distinguished from cultural conditioning. This is evident, for example, in biblical texts (such as Ex. 21:20-21) and in some magisterial interventions that tolerated slavery (Cf. Nicholas V, Bull Dum Diversas [1452]). This is not a minor issue, given its intimate connection with the perennial truth of the inalienable dignity of the human person. These texts require an interpretation. The same applies to certain considerations in the New Testament regarding women (1 Cor. 11:3-10: 1 Tim. 2:11-14) and to other texts of Scripture and testimonies of Tradition that cannot be materially repeated today.
As an aside, note above how exceptionally liberal Pope Francis's view of the Bible is, wherein he says that 1 Corinthians 11:3-10, and 1 Timothy 2:11-14, among "other texts of Scripture", "cannot be materially repeated today".
Catholic Apologist Paul Kengor also seems to conclude that these Bulls of Nicholas V supported slavery, though he appeared to run into dead ends in his research attempting to further contextualize them:
Paul Kengor - The Catholic Church and Slavery
Well, the church has been so consistent on this for so long, and the only example that I can find where a pope failed was probably Nicholas the V with two statements Dum Diversas and Romanus Pontifex, which so confounds modern scholars. I literally emailed over 100 Catholic scholars, and I counted, trying to figure out, trying to make sense of what he was trying to say with these two statements that he had.
It is clear historically that there was Portuguese enslavement of West Africans during and after the pontificate of Pope Nicholas V. One essay says over 100,000 slaves were exported to Europe and America during the period 1415-1600, not counting resident slaves who stayed in West Africa. Another essay entitled Pope Nicolas V and the Portuguese Slave Trade also recognizes that chattel slavery was practiced by the Portuguese in West Africa.
So, it seems that chattel slavery being practiced by the Portuguese, in part due to these Papal Bulls, is uncontroversial, historically speaking.
Later, Pope Alexander VI (1431-1503 AD) would issue the Papal Bull Eximiae Devotionis (1493 AD), which extended to Spain the rights that Pope Nicholas V had conferred to Portugal:
Pope Alexander VI - Eximiae Devotionis (1493 AD)
Moreover we extend similarly, and enlarge these powers, in all things and through all things to you and your aforesaid heirs and successors, to whom in the same manner and form we grant them forever, apostolic constitutions and ordinances as well as all grants of similar kind made by letters to the kings of Portugal, as well as other things whatsoever to the contrary not withstanding.
The above is significant, because it was addressed to King Ferdinand and Queen Isabella of Spain, who are famous for their sponsoring of Christopher Columbus, who discovered the new world, and who was himself notorious for how abominably he treated native slaves that he and his envoy took.
The Roman Catholic Church has contradicted itself on the issue of slavery. In modern times, they denounce it as an immoral abuse which is an affront to human dignity. However, in the past, it issued decrees which allowed or even explicitly encouraged enslavement, and a total ban on slavery did not come until rather recently in Church history:
Pope Francis - Fratelli Tutti (2020 AD)
86 I sometimes wonder why, in light of this, it took so long for the Church unequivocally to condemn slavery and various forms of violence. Today, with our developed spirituality and theology, we have no excuses.