[RFC] Logger_connector should own the logger, and should not have a Trainer reference

[daniellepintz]

Proposed refactor

• Create a logger property on the logger_connector
• Create a read-only property on the Trainer called logger which returns logger_connector.logger
• Remove Trainer reference from logger_connector

Motivation

• Currently the Trainer owns the logger, but it is configured/set in the logger_connector:
  https://github.com/PyTorchLightning/pytorch-lightning/blob/32e7d32956e1685d36f2ab0ca3770baa2f76ce10/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py#L78-L91
• The logger should be written to in the same class where it is owned
• The Trainer class is already giant and does a lot, so let's have the logger_connector own all things related to the loggers, including the loggers themselves. (We will still have a read-only property for the loggers on the Trainer)
• This approach is similar to what we do for the accelerator_connector. The accelerator_connector owns the accelerator related properties, and has no reference to the Trainer.

Part of #10417

Pitch

• Create a logger property on the logger_connector
• Update all the reference of trainer.logger on the logger_connector to self.logger
• Create a read-only property on the Trainer called logger which returns logger_connector.logger
• Update all the other places where the trainer is used in logger_connector - some variables will have to be passed in the constructor, and others will have to be passed as arguments to some methods such as should_flush_logs
• Remove Trainer reference from logger_connector

cc @justusschock @awaelchli @akihironitta @rohitgr7 @edward-io @Borda @ananthsub @kamil-kaczmarek @Raalsky @Blaizzy @kaushikb11 @ninginthecloud

[awaelchli]

That would be really nice to have!