Improve typing coverage

[tchaton]

Please make one PR per file!

The list of pending files is can be found below here

https://github.com/Lightning-AI/lightning/blob/master/pyproject.toml#L39-L43

cc @Borda @justusschock @awaelchli @akihironitta @rohitgr7

[Borda]

Duplicate to #5023

[akihironitta]

#7035 (comment)

Open for discussion: Should we also type the tests? I don't think we have to!

I don't think we need type annotations in the tests, but we should run mypy to check if variables/functions of the package are correctly typed. What do you think?

[stancld]

After the chat with Eden, I'll tackle lightning.utilities :)

[stancld]

Hello @tchaton, I noticed new information about making one PR per file was added to the first comment. As I've been dealing with some mypy issues, my PR #7218 has become quite heavy. Is it, therefore, appropriate to close this PR, though already with a few reviews given, and open new ones separately for each file? Thanks :)

[Borda]

@tchaton what is the status here? 🐰

[kingjuno]

@tchaton Can I work on these 3?
pytorch_lightning.callbacks.finetuning
pytorch_lightning.callbacks.model_checkpoint
pytorch_lightning.callbacks.progress.rich_progress

[otaj]

@kingjuno, you're more than welcome to help! We are closing this issue in favor of #13445 in order to promote better visibility, please feel free to comment there.