During Constantine's time art and architecture were still recognisably Roman as we know it, with realistic sculptures and classical style buildings. Yet barely 2 centuries later, Justinian's famous portrait in gold mosaics looks like a bloody anime figure with unrealistically big eyes. Gone are the grandiose buildings decked out in marble, replaced by buildings like the Hagia Sofia and the San Vitale Church that don't look all that Roman even before the minarets. Renaissance art meanwhile obviously has its roots in classical antiquity. While I can appreciate it on its own, how did Byzantine art culture stray so far from its Roman roots?
Also I have zero academic background in either history or art so please feel free to correct me.
Before I answer your question, I think it's worth pointing out that there's some misconceptions here. Most of the developments you're describing had already taken place by the time of Constantine the Great:
with unrealistically big eyes
Constantine's own statue in the Basilica Nova in Rome, likewise sported cartoonishly large eyes, the same goes for many Emperors in the Tetrarchy which preceeded Constantine, such as Galerius (293-311) and Maximinus Daia (305-313).
Infact the contrast between the art of the 2nd Century and the 4th is best exemplified on the Arch of Constantine, in Rome. This arch was erected by the Senate in 315, following Constantine's victory over Maxentius, and used a considerable amount of spoila (reused sculpture from older buildings). In this picture you can see the roundels on the upper half, which are taken from the time of Hadrian, compared to the comparatively simple Constantinian reliefs on the bottom half. It's clear that by the time of Constantine, the popular artistic style had already shifted away from realism.
Gone are the grandiose buildings decked out in marble, replaced by buildings like the Hagia Sofia
This is a bit of a strange statement, because the Hagia Sophia is decked out in tons of finely carved marble, in classical patterns. Even the Hagia Sophia's exterior was fully or partially covered in marble, some of which has been found and remounted on the entrance facade.
Now, while I don't agree that later Roman art swayed away from marble revetment and classical decorative motifs, there was a clear move away from realism, particularily in sculpture, even if this predates Constantine.
Older scholarship tended to conclude that this stylistic shift occured due to a loss in material culture. That the Romans of the 4th and 5th Centuries simply didn't have the the ability to make this type of art anymore, that the skills had been lost, which is why they had to use so much spoila.
There are still some that subscribe to this theory, but the main problem with this explanation is that it can't be reconciled with the many pieces of more classical art from the later periods, here are some examples:
-Statue of Emperor Julian, late 4th Century
It seems pretty evident from these examples that Romans in the 4th, 5th and even 10th Centuries could make more realistic, proportionate, classical art. But chose instead to focus more on the abstract styles. This seems to suggest that the ability to make these was not lost, and that it was rather a concious stylistic preference.
This may have occured due to an increased trade with the east, in particular with Sassanian Persia, which had similar aesthetics in their art. It may also have occured due to an increased interest in spirituality, that the art wasn't supposed to depict things the way they actually looked, but instead it was supposed to portray the feeling of the moment. Baby Jesus for example, in much medieval artwork tends to look like a tiny adult man instead of an actual baby. This doesn't mean they thought Baby Jesus looked like that, it's merely supposed to portray that Jesus was wise beyond his age, even as an infant.
If you have any follow-up questions or want me to clarify/elaborate some of my points, feel free to ask.
