Twice in the Quran, Muhammad gives an account of the creation of mankind by God, and it is an account of special creation directly from mud/clay, which also includes a story of the Devil refusing to worship Adam, borrowed from a late apocryphal Jewish work from before the time of Muhammad called The Life of Adam and Eve:
Surah 15:26-33
26 Indeed, We created man from sounding clay moulded from black mud.
27 As for the jinn, We created them earlier from smokeless fire.
28 ˹Remember, O Prophet˺ when your Lord said to the angels, "I am going to create a human being from sounding clay moulded from black mud.
29 So when I have fashioned him and had a spirit of My Own ˹creation˺ breathed into him, fall down in prostration to him."
30 So the angels prostrated all together -
31 But not Iblîs, who refused to prostrate with the others.
32 Allah asked, "O Iblîs! What is the matter with you that you did not join others in prostration?"
33 He replied, "It is not for me to prostrate to a human You created from sounding clay moulded from black mud."
Surah 38:71-72
71 ˹Remember, O Prophet˺ when your Lord said to the angels, "I am going to create a human being from clay.
72 So when I have fashioned him and had a spirit of My Own ˹creation˺ breathed into him, fall down in prostration to him."
The Quran also contains multiple other verses stating that mankind was created from clay/dust (Surah 6:2, 18:37, 22:5, 23:12, 30:20, 32:7, 35:11, 37:11, 40:67, 55:14).
Therefore, the issue of whether Islam is compatible with the modern theory of Evolution is rather straightforward. Its primary scripture presents multiple accounts of the direct creation of mankind by God, which is clearly borrowed from an older Jewish legend of the creation of Adam, who is the progenitor of the whole human race in Judaism (Genesis 2:5-8: 1 Chronicles 1:1), and Islam (Surah 4:1, 6:98, 7:189, 39:6, Sahih al-Bukhari 3431, 3334, 6529, 6614, 7516, etc.). And, it presents zero accounts whatsoever of mankind or any other creature evolving from lower species over millions of years.
The religion of Islam is incompatible with Evolution - or rather, it is refuted by the overwhelming evidence for Evolution (endogenous retroviruses, DNA similarity, etc.), which demonstrates that mankind evolved from lower species, and was not created from mud/clay.