Simple CloudWatch logger

Nobody has claimed this yet.

### Description & Motivation

I'm using pytorch lightning and and torchmetrics for training. It works great on my local device and on AzureML - the tensorboard/mlflow loggers implemented in lightning do the job very well.

Recently I started training models on Sagemaker, and I don't see an easy/clean way to log metrics and track experiments in CloudWatch.

### Pitch

Recently I started training models on Sagemaker. I'd like to be able to track the training metrics while training directly in CloudWatch. To enable this, I've added `print()` to my code, which is ugly:
```
# Example of a training_step that's agnostic to the way the model is trained
def training_step(self, batch, batch_idx):
images, labels = batch
outputs = self(images)

# Loss
loss_value = self.loss(outputs, labels)
self.log('train_loss', loss_value, on_step=True, on_epoch=True)

# From outputs, get the class with the highest probability
predictions = torch.argmax(outputs, dim=1)

# Log metrics
self.train_accuracy(predictions, labels)
self.log('train_accuracy', self.train_accuracy, on_step=False, on_epoch=True)

# Save training_step_outputs -> added for CloudWatch support
self.training_step_outputs.append((loss_value, predictions, labels))

return loss_value

# For logging to CloudWatch, I need to write the logs manually
def on_train_epoch_end(self):
training_step_outputs = self.training_step_outputs
#... calculate metrics ...

print(f"train_loss:{train_loss};")
print(f"test_acc: {test_acc};")

self.training_step_outputs.clear() # free memory
```

In sagemaker related code, I specify the metrics regexes to match the print statements:

```
estimator = PyTorch(
# Some standard code
# ...

metric_definitions=[
{'Name': 'train_loss', 'Regex': 'train_loss:(.*?);'},
{'Name': 'train_accuracy', 'Regex': 'train_acc:(.*?);'},
],
enable_sagemaker_metrics=True,

)

```

I'd like to propose an implementation of a CloudWatch logger. It would:
- log every metric as `print(f'{metric_name}:{metric_value}')

Are there any suggestions how logging to CloudWatch could be more easily supported?

If this proposal makes sense to the commynity, I can implement the logger and create a PR.

### Alternatives

Add `print` statements to the `on_train_epoch_end`, as mentioned above.

### Additional context

_No response_

cc @borda @awaelchli @Blaizzy

Start by reviewing the existing TensorBoard and MLflow logger implementations mentioned in the issue, then compare their metric lifecycle with the example training_step and on_train_epoch_end hooks. The issue provides no repository files or tests; done would require an agreed CloudWatch logger scope and metrics that work with the shown SageMaker metric_definitions.

Written by the indexing model from the issue text.