A new version of 1.16.5 Pixelmon came out, so I tested it, and eureka: Out-of-battle catches have been fixed, and we can now resume regular updates.

However, our latest build 0.6.18 said that it contained versions of mods that aren't on Curseforge. I can't figure out which mod that is, as they all say they are up-to-date, so I'm creating a new modpack and re-adding in the mods one-by-one to see which one broke things.

Fixed. It was a pixelmon spawning file that shouldn't have been in the mod folder.

Actually, now that I think about it, it's probably still a good idea to do a mod flush, in order to get rid of anything we don't strictly need that was added during testing.