The supposed Islamic rules against illustrations of living things are far more limited than people popularly imagine. They have only ever applied in very specific places and times. For example, in the Persian-speaking world (Iran, Central Asia, India), under both Sunni and Shi'ite regimes, there was never a historic proscription on illustrating anything other than the face of the prophet - and even this rule was not universally adhered to. Arabs were more likely to avoid depiction, but it was by no means a universal rule. One of the most common translated and reproduced works in the classical Islamic world was De Materia Medica, and books like this were often illustrated. Here is an example at the Met.
Now, that said, medical instruction generally would have been based on hands-on experience, lectures, and un-illustrated manuscripts. But the reason was less the rule against illustration than the price of illustration. Illustrated books were prestigious luxury items in the Islamic world, as they were elsewhere, and were not generally available on a student budget. Dissection on the other hand was not a normal part of the medieval Islamic world any more than it was part of the Christian world, and cutting-edge medical theory was generally still based on Galen. Being the foremost seat of science and knowledge didn't mean doing things in what we'd currently recognize as a scientific way, with experiments and observation and falsifiable hypotheses. Here is an article on dissection and Islam at JSTOR if you have access, and here is an (open-access) article on one specific type of anatomical illustration (optics).
The answer presented by r/thither_and_yon is great, but I want to add more about the opinion of Sunni Islamic jurisprudence regarding the ban on illustration of living things.
1- Islamic jurisprudence has two main sources: Quran, the holy book revealed to Muhammad over the course of the last 23 years of his life, which is memorized by Muslims and has been preserved word for word and letter for letter over the centuries. Muslims believe that the text itself is the literal word of God (Allah, in Arabic). The second source is the Sunnah, narrations of the words, actions and approvals of the prophet himself written by his companions (Hadiths). This is comparable to the Christian New Testament, i.e. the texts are much wider in scope than the Quran and less preserved in general. The text of the Sunnah is not considered sacred in itself, unless it is proven authentic by the scholars of Hadith.
2- The ban against illustrations of living animals/humans was not mentioned in the Quran itself, but was mentioned in several Hadiths. For example:
a- It was narrated in Musnad Ahmad (part 2/ hadith no. 305) that Abu Huraira said that he heard the Prophet say: "Jibril (the Archangel Gabriel) told me: "I wanted to visit you last night, but what prevented me from entering your house was the presence of the statue of a man, a curtain that has drawings (of living things) and a small dog." So, I ordered the statue's head to be broken, the curtain to be made into pillows to be stepped on and the dog to be let outside of the house."
b- Al-Bukhari and Muslim both narrate the Ibn Abbas said: "The prophet said: "Whoever made a Surah (statue/illustration), God will keep tormenting him until he can breathe life into his Surah, and he will never be able to.", so if someone wants to keep making Surahs, then make Surahs of plants or trees instead. "
3- From these Hadiths and many others we can deduce the following:
a- The forbidden illustrations are those of Humans and Animals, not plants and not non-living things.
b- Statues of animals and humans must be broken so that they are not complete, such as breaking the head in the first hadith.
c- Drawn illustrations of animals and humans can be made into things that are not revered/respected such as pillows/rugs .. etc. But not hanged such as paintings or curtains.
d- Many of the Muslim Scholars agree that this ban was due to the wide spread of idol worshiping and religious iconography, representing a form of Iconoclasm (similar to the movement that was present in the Byzantine empire at the same time).
4- From this you can see that medical and scientific illustrations do not fall under the category of revered illustrations or iconography, nor they fall under the category of statues. Therefore, these illustrations made for practical or educational purposes were not forbidden or frowned upon. One of the most famous example of educational illustrations is the "Book of Animals" written by the early Muslim Scholar Al-Jahiz (776 - 868 CE), which was written as a sort of early Zoology book, and included a lot of pictures of human and animals such as this.
