Separate validation precision in trainer arguments

Nobody has claimed this yet.

### Description & Motivation

The trainer should have a separate precision parameter for training and validation.

The feature would allow trading validation speed for some loss of measurement exactness. This is useful when validation takes a noticeable fraction of the overall training time. This scenario is common when training language models (e.g., language translators), where the model quality is measured by comparing *autoregressively generated* outputs with reference sequences.

### Pitch

The functionality would be exposed via `precision_val` parameter:

```python
trainer = lightning.Trainer(
precision="16-mixed",
precision_val="16-true"
)
```

### Alternatives

The user might implement custom precision logic in `on_validation_start` and `on_validation_end` callbacks in their `LightningModule`.

However, `Lightning` seems to generally advise against using `.to(device, dtype)` to manipulate model/tensors representation in memory because `Lightning` itself handles that, so writing custom precision logic in `LightningModule` appears out-of-place and error-prone.

### Additional context

For inspiration, `Seq2SeqTrainer` in the `transformers` library supports the proposed functionality via `fp16_full_eval=True` and `bf16_full_eval=True` parameters.

Relevant docs: https://huggingface.co/docs/transformers/en/main_classes/trainer#transformers.Seq2SeqTrainingArguments.fp16_full_eval

cc @lantiga @borda

Start by tracing how the Lightning Trainer currently handles the precision parameter across training and validation. Compare the proposed behavior with Transformers' Seq2SeqTrainer options and the documented on_validation_start/on_validation_end callback alternative; done means a separate precision_val setting controls validation without changing training precision.

Written by the indexing model from the issue text.