…el checkpointing separately in new state.best_metric_checkpoint variable

What does this PR do?

Fixes # (issue)

Before submitting

• [x] This PR fixes a typo or improves the docs (you can dismiss the other checks if that's the case).
• [x] Did you read the contributor guideline, Pull Request section?
• [x] Was this discussed/approved via a Github issue or the forum? Please add a link to it if that's the case.
• [ ] Did you make sure to update the documentation with your changes? Here are the documentation guidelines, and here are tips on formatting docstrings.
• [ ] Did you write any new necessary tests?

Who can review?

Anyone in the community is free to review the PR once the tests have passed. Feel free to tag members/contributors who may be interested in your PR.

As suggested here: https://github.com/huggingface/transformers/issues/16620

TODO: appropriate tests

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This issue has been automatically marked as stale because it has not had recent activity. If you think this still needs to be addressed please comment on this thread.

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