Use the Callback state_key to disambiguate callbacks provided to trainer and from LightningModule

Nobody has claimed this yet.

We still use the types of the callbacks here: https://github.com/PyTorchLightning/pytorch-lightning/blob/92d9fc2280091c300fe8848284b9f6dfcbd209eb/pytorch_lightning/trainer/connectors/callback_connector.py#L272-L283

This can lead to collisions, when perhaps we have multiple callback instances of the same type with different settings that we want to use together.

For checkpointing callback states, we have shifted to using the newly introduced callback state key here: https://github.com/PyTorchLightning/pytorch-lightning/blob/92d9fc2280091c300fe8848284b9f6dfcbd209eb/pytorch_lightning/trainer/callback_hook.py#L58

We can do the same thing in this callback connector

_Originally posted by @ananthsub in https://github.com/PyTorchLightning/pytorch-lightning/pull/11060#discussion_r768986581_

cc @justusschock @awaelchli @akihironitta @rohitgr7 @ananthsub @daniellepintz

Start in pytorch_lightning/trainer/connectors/callback_connector.py at the callback handling around lines 272-283, then read the state-key usage in pytorch_lightning/trainer/callback_hook.py around line 58. Trace how callbacks supplied to the Trainer and LightningModule are distinguished. Done means multiple instances of the same callback type with different settings can be used together without collisions.

Written by the indexing model from the issue text.