Enable dumping raw prof files in AdvancedProfiler

[clumsy]

What does this PR do?

Adding a new dump_stats flag to AdvanedProfiler to persist .prof files collected during profiling. These files can be visualized by SnakeViz like so: snakeviz fit-run-[Strategy]DDPStrategy.on_train_end.prof

A .prof file is created for each profiled action, e.g.:

...
fit-run-[Strategy]DDPStrategy.on_train_end.prof
fit-run-[Callback]TQDMProgressBar.on_fit_end.prof
fit-run-[Callback]ModelSummary.on_fit_end.prof
fit-run-[Callback]ModelCheckpoint{'monitor': None, 'mode': 'min', 'every_n_train_steps': 0, 'every_n_epochs': 1, 'train_time_interval': None}.on_fit_end.prof
fit-run-[Callback]LearningRateMonitor.on_fit_end.prof
...

Fixes #19698

No breaking changes, adding a new backward-compatible flag, with the new functionality disabled by default.

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📚 Documentation preview 📚: https://pytorch-lightning--19703.org.readthedocs.build/en/19703/

[clumsy]

For your consideration, @awaelchli

[clumsy]

Are there any concerns about this change, @awaelchli? Thanks!

[clumsy]

Just bumping this one in case it got lost in notifications, @awaelchli.

[awaelchli]

@clumsy Looks great to me. Just a few minor comments

[clumsy]

Thanks for checking, @awaelchli! I've addressed your comments. Please let me know if the are remaining concerns.

[awaelchli]

@clumsy Are you still interested in finishing the PR? I think it's very close to land.

[clumsy]

Sure, addressed the comments, @awaelchli

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 82%. Comparing base (2dc9c3d) to head (4dfc086).
Report is 55 commits behind head on master.

❗ There is a different number of reports uploaded between BASE (2dc9c3d) and HEAD (4dfc086). Click for more details.

HEAD has 85 uploads less than BASE

Flag	BASE (2dc9c3d)	HEAD (4dfc086)
cpu	40	21
lightning	33	17
pytest	25	3
python3.9	12	6
python3.10	11	6
python3.11	12	6
lightning_fabric	6	0
gpu	6	3
python3.12	5	3

Additional details and impacted files

@@            Coverage Diff            @@
##           master   #19703     +/-   ##
=========================================
- Coverage      91%      82%     -9%     
=========================================
  Files         266      263      -3     
  Lines       22968    22931     -37     
=========================================
- Hits        20799    18755   -2044     
- Misses       2169     4176   +2007     

[awaelchli]

Nice @clumsy thank you for addressing the remaining comments.