📚 TODOs around the loop refactor

This issue tracks the work planned for and after the loop refactor #7700.
Core contributors feel free to update the description here directly.

Hygiene and code quality

• Typing for full mypy compatibility (see ignored files in setup.cfg)
• Documentation for the public interface + address [Refactor] Remove _run_evaluation + 3 EvaluationLoop #8065 (comment)
• Evaluate which methods should be public and which should be protected
• Rename Trainer.train_loop to Trainer.fit_loop and deprecate the former access.
• Formalize how arguments are forwarded to lower loops (especially in connect

Feature integration and follow-up refactors

• Extract a OptimizerLoop, potentially a loop for TBPTT extract optimizer loop #9191
  • extract utility for _run_optimization
  • for manual optimization, replace closure call with direct call to _training_step()
• Integrate progress tracking Formalize progress tracking inside of the trainer internals #6429, this will also increase clarity and minimize attack surface for bugs!
• Determine who should own the dataloaders and responsibility of resetting them Loop Refactor 1/N - Training Loop #7871 (comment). Can references fall out of sync? Loop Refactor 1/N - Training Loop #7871 (comment)
• Add a teardown, let loops move their results to CPU instead of LoggerConnector: Move result teardown to loops #8245
• The EvaluationDataLoaderLoop.predictions are currently accumulated inside the inner evaluation loop instead of per epoch and then combined over all dataloaders. Remove write_predictions from LightningModule #8850
• Rename inner loops to epoch_loop, batch_loope etc to distinguish top level loop access. Also propose file structure organizing these. Resolved by pytorch_lightning.loops file structure: group by dataloader, epoch, and batch loop  #8077

Customization

• Formalize how loops get instantiated, set on the trainer, and connected to each other. Loop specialization #8226

Miscellaneous

• Several todo's are annotated as TODO(@awaelchli)
• Some todo's are annotated as TODO(@justusschock) as well.

cc: @justusschock @carmocca @ananthsub @tchaton