My recollection when I was once studying physics and looking into this is that some interpretations of QM do entail or allow for absolute simultaneity. Some do not, such as the prevalent Copenhagen interpretation.

This article from 2009 discusses these kinds of matters, and near the end it talks about absolute simultaneity:

"The kind of nonlocality one encounters in quantum mechanics seems to call for an absolute simultaneity, which would pose a very real and ominous threat to special relativity."

https://www.scientificamerican.com/article/was-einstein-wron...