Fix MLflowCallback and add support for MLFLOW_EXPERIMENT_NAME
# What does this PR do?

This PR includes the following:
- Resolves #12841: uses the MLFLOW_EXPERIMENT_NAME environment variable and the mlflow.set_experiment() method to ensure the experiment is created if it does not exist already.
- Fixes #17066: Checks properly for an active run using mlflow.active_run() (Bug introduced in #16131).

Supersedes #17067 due to CI build errors.

## Before submitting
- [ ] 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](https://github.com/huggingface/transformers/blob/main/CONTRIBUTING.md#start-contributing-pull-requests),
      Pull Request section?
- [ ] Was this discussed/approved via a Github issue or the [forum](https://discuss.huggingface.co/)? Please add a link
      to it if that's the case.
- [x] Did you make sure to update the documentation with your changes? Here are the
      [documentation guidelines](https://github.com/huggingface/transformers/tree/main/docs), and
      [here are tips on formatting docstrings](https://github.com/huggingface/transformers/tree/main/docs#writing-source-documentation).
- [ ] 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.

@sgugger 
_The documentation is not available anymore as the PR was closed or merged._<|||||>Managed to activate the test by checking out your PR and pushing it to a new branch in the `transformers` namespace. I have no idea why it worked.

Anyhow, please run `make style` on your branch to fix the code quality issue and we should be good to merge! (you'll need to install the latest versions of our deps for styling with `pip install .[quality] -U` )<|||||>@sgugger All checks passed! 🤗 <|||||>Thanks a lot!