Introduce training and eval modes for the strategy

Nobody has claimed this yet.

### Description & Motivation

Some of our strategies need to be set up differently depending on whether the model is being trained or just evaluated (`.fit` vs `.test`).

Some examples:

https://github.com/Lightning-AI/lightning/blob/859a228a915893f14759dda6d35f6050fe6df382/src/pytorch_lightning/strategies/ddp.py#L170-L173

https://github.com/Lightning-AI/lightning/blob/859a228a915893f14759dda6d35f6050fe6df382/src/pytorch_lightning/strategies/ddp.py#L357-L363

https://github.com/Lightning-AI/lightning/blob/859a228a915893f14759dda6d35f6050fe6df382/src/pytorch_lightning/strategies/ipu.py#L146-L149

This requires us to pass in the entire Trainer instance just to check the stage. Unifying this with the base strategies from Lite is not possible, because of the dependency on Trainer.

### Pitch

Introduce `strategy.train()` and `strategy.eval()` with a similar mechanism as in `nn.Module.train/eval()`. This could be a method or a boolean attribute. The call to change this state would happen in the training loop/the trainer.

For now, this proposal would only be for the strategy definition in Trainer. This helps us standardize the interface for both strategies, while maintaining the flexibility of adding Trainer-specific logic outside Lite.

### Alternatives

Alternatively, the state could be passed in to the individual methods of the strategy.

### Additional context

_No response_

cc @borda @justusschock @carmocca

Start by reading the referenced strategy examples in src/pytorch_lightning/strategies/ddp.py and src/pytorch_lightning/strategies/ipu.py, then trace how the Trainer or training loop currently determines the stage. Done means strategies have a standardized training/evaluation state without requiring the entire Trainer just to inspect it.

Written by the indexing model from the issue text.