I've submitted a bug report to Epic. They have not responded. My hands are sadly tied, as it's an issue in the core of the engine that I can not fix from the outside.
The current spine-ue4 runtime works with UE 5.3 provided that your skeleton and atlas files do not share the same name up until the extension. E.g. skeleton.skel and skeleton.atlas will not work. However, skeleton-foo.skel and skeleton.atlas will work.
The issue is mostly with old projects that want to migrate to UE 5.3. If the asset files have common prefixes as shown above, there's literally no way for our plugin to fix this automatically. I could not even find a way to fix it manually. That's how bad this situation is.
So, people may not be able to ever upgrade to UE 5.3 depending on Epic. New projects can follow the "no common prefix" pattern and use UE 5.3+.