Fix/best model checkpoint fix
Author: seanswyi
Pull request: yes

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Fixes https://github.com/huggingface/transformers/issues/35609 (TL;DR `best_model_checkpoint` is being set when the checkpoint may not even exist)

- Add a new attribute to TrainerState called `best_global_step` that keeps track of the step where we performed evaluation and achieved a new best metric.
- Moved setting `best_model_checkpoint` from `_determine_best_metric` to `_save_checkpoint`.
- Inside `_save_checkpoint`, check if the `best_model_checkpoint` actually exists, and set it if so.

This was a bit trickier than I thought it would be, since the Trainer's saving and evaluation logic are not tightly coupled as would be in the `save_strategy == "best"` scenario.

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Comments:
tests/trainer/test_trainer.py::TrainerIntegrationTest::test_best_model_checkpoint_behavior test you created is failing, can you check ? 

The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/transformers/pr_35885). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

> tests/trainer/test_trainer.py::TrainerIntegrationTest::test_best_model_checkpoint_behavior test you created is failing, can you check ?

I think the error should be fixed now. Problem was I had hardcoded values and wasn't using the patch correctly. Thanks for pointing it out.

Make sure to run make style for the CI. There is also a failing test but that's unrelated to this PR 

> Make sure to run make style for the CI. There is also a failing test but that's unrelated to this PR

Done. I'm not sure why but there was a bit of discrepancy between my local setting and the CI pipeline so I had to make the changes through a Docker image since `make style` wasn't working.

thanks ! i will wait for @tomaarsen to test the PR before reviewing it 

I haven't reviewed the code in this PR, but I can confirm that my test passes with this branch again!
cc @SunMarc 

- Tom Aarsen