Introduce `Logger.experiment_dir`

[tshu-w]

"## What does this PR do?

Introduce the property first.

Part of #14188

Next steps:

1. Change Trainer.log_dir to experiment_dir and ModelCheckpoint Implementation #14640,
2. Update implementations of some Loggers, and maybe drop some unnecessary properties(name, version, etc)
3. Introduce Trainer.experiment_dir and deprecate Trainer.log_dir

Does your PR introduce any breaking changes? If yes, please list them.

When the Logger.save_dir is None (DummyLogger, CometLogger(online), Deprecated LoggerCollection, etc), the Trainer.log_dir is None either, and the checkpoints directory is default_root_dir/name/version. https://github.com/Lightning-AI/lightning/blob/b33e3ef18aa8f50dd905e3762aaaa3117aa65705/src/pytorch_lightning/callbacks/model_checkpoint.py#L594-L604

Since there are many Loggers that can have a save_dir of None, I prefer to make logger.experiment_dir return a relative path. cc @awaelchli

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Did you have fun?

Make sure you had fun coding 🙃 "

[carmocca]

If this is going to be sequenced so the properties are introduced first, and then used. I would like that you open the follow-up PR already so that we can see that things worked as expected (CI passed).

[tshu-w]

If this is going to be sequenced so the properties are introduced first, and then used. I would like that you open the follow-up PR already so that we can see that things worked as expected (CI passed).

Sure, I can open the following PR first. Should I make this to draft PR first?

[codecov[bot]]

Codecov Report

Merging #14508 (b33e3ef) into master (b33e3ef) will not change coverage. The diff coverage is n/a.

:exclamation: Current head b33e3ef differs from pull request most recent head a1119c1. Consider uploading reports for the commit a1119c1 to get more accurate results

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