I just had a quick look at a couple of Jira instances that I’m working on, and they’re all still using the old config with a UI with Epic Link showing, so it looks like the change-over hasn’t started in our region yet.
Are you not able to contact the sys admins for those few problem Jira instances and ask them how their instance is configured? It would a great way to know for sure. You could also run a query against the Get field configurations endpoints to find out what fields they have, what screens are using them and which projects are using those screens. You’d then know if the Epic Link field is active and on the appropriate screens for the projects you are running the JQL against.
Personally, I stopped using both Epic Link and Parent Link fields about 6 months ago, when the deprecation notice came out, so all my code now uses Parent field and I’ve not had any issues, plus I’m future-proofed when the change comes to my region.
Good luck with finding the answer, and please post it here when you work it out.