Aurora forked PostgreSQL very early on (before 9.6) and has been improved independent and a lot has been changed. They are effectively different databases now.
They changed the storage layer and the query planner in some parts to work correctly with their new storage layer. So it‘s a fork and not behaving exactly identical. I have seen some different execution plans for the same model and data because of the implications pf the changed storage layer and query optimizer.
Do you know of any credible source for Amazon forking postgresql? I did some googling and can certainly find lots of people saying it, but nothing authoritative from Amazon themselves.
AWS is basically never sharing any details, only when it‘s benefical in terms of marketing. The changes they made had not been possible with an extension in the past, and they are most probably still not fully possible without forking. But thats not problem, they are free to fork and merge upstream changes.
For MySQL any of the big users like facebook & co. Are running (heavy) forked mysql versions with changes they need.