[3.x] Backport new pause modes

[KoBeWi]

Non-compatibility-breaking backport of #46191

The PR just adds 2 new pause modes:
PAUSE_MODE_STOP_ALWAYS -> same as PROCESS_MODE_DISABLED in 4.0
PAUSE_MODE_PROCESS_PAUSED -> same as PROCESS_MODE_WHEN_PAUSED in 4.0
Everything else is the same.

I tested with AnimationPlayer and the new pause modes work as expected, even when inherited.

[KoBeWi]

Ok, as it turns out, the fact that it worked for AnimationPlayer was a coincidence. Some nodes seem to just use can_process(), so for them this will work. But some nodes rely on NOTIFICATION_PAUSED and NOTIFICATION_UNPAUSED. The original PR sends the notification after pause mode changes. I could backport that too, but it slightly breaks compatibility I guess 🤔 Not sure if that's acceptable.

EDIT:
I tried to implement it, but it requires more changes and causes more problems than it's worth. Also the current pause modes are broken anyways (#58543, probably applies to all similar nodes)

[akien-mga]

So it sounds like this isn't working properly yet? Is it still worth attempting for 3.6 or should we shelve it?

[KoBeWi]

I think it should work correctly after #58577 is merged.

[ande8133]

This would be a great feature to have. Any update on this?

[KoBeWi]

Well, #58577 was merged, so this might be functional now, but I didn't test. I'm not really interested in this feature anymore, so feel free to take over.