Refactor RunningStage routing mechanism

[tchaton]

🚀 Feature

Motivation

Currently, tes / predict function is relying on an ENV variable to set testing to True.

The logic should be simplified and cleaned up.

Pitch

Additional context

No we can't in the current state of the codebase. Trainer.predict relies on self.trainertesting to be True for routing the code in the test part of the evaluation loop, and if we set self._running_stage = RuningStage.PREDICTING, it would route to validation and we won't gather the prediction.
I plan to properly refactor routing in a follow up PR as it is currently a big mess.

Originally posted by @tchaton in #5579 (comment)

[rohitgr7]

which env variable?

[awaelchli]

@carmocca I believe this can be closed because you have worked on this just recently in #4945, right?

[carmocca]

Yes!