TrainingArguments no longer sets `ACCELERATE_MIXED_PRECISION` environment variable
Author: Thytu
Pull request: yes

# What does this PR do?

TrainingArguments no longer sets `ACCELERATE_MIXED_PRECISION` environment variable and instead relies on newly added `AcceleratorConfig.mixed_precision` attribute. This prevents cases where mixed precision was activated even when Training arguments wasn't provided to `Trainer`.

* AcceleratorConfig now contains a new attribute named `mixed_precision`

* TrainerArguments no longer sets `ACCELERATE_MIXED_PRECISION` environment variable

* TrainerArguments sets AcceleratorConfig.mixed_precision attribute according to received arguments

* TrainerArguments sets deep_speed mixed precision even when activated through ACCELERATE_USE_DEEPSPEED env variable

<!--
Congratulations! You've made it this far! You're not quite done yet though.

Once merged, your PR is going to appear in the release notes with the title you set, so make sure it's a great title that fully reflects the extent of your awesome contribution.

Then, please replace this with a description of the change and which issue is fixed (if applicable). Please also include relevant motivation and context. List any dependencies (if any) that are required for this change.

Once you're done, someone will review your PR shortly (see the section "Who can review?" below to tag some potential reviewers). They may suggest changes to make the code even better. If no one reviewed your PR after a week has passed, don't hesitate to post a new comment @-mentioning the same persons---sometimes notifications get lost.
-->

<!-- Remove if not applicable -->

Fixes #29510

## 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#create-a-pull-request),
      Pull Request section?
- [X] 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.

@muellerzr & @amyeroberts

<!-- Your PR will be replied to more quickly if you can figure out the right person to tag with @

 If you know how to use git blame, that is the easiest way, otherwise, here is a rough guide of **who to tag**.
 Please tag fewer than 3 people.

Models:

- text models: @ArthurZucker and @younesbelkada
- vision models: @amyeroberts
- speech models: @sanchit-gandhi
- graph models: @clefourrier

Library:

- flax: @sanchit-gandhi
- generate: @gante
- pipelines: @Narsil
- tensorflow: @gante and @Rocketknight1
- tokenizers: @ArthurZucker
- trainer: @muellerzr and @pacman100

Integrations:

- deepspeed: HF Trainer/Accelerate: @pacman100
- ray/raytune: @richardliaw, @amogkam
- Big Model Inference: @SunMarc
- quantization (bitsandbytes, autogpt): @SunMarc and @younesbelkada

Documentation: @stevhliu and @MKhalusova

HF projects:

- accelerate: [different repo](https://github.com/huggingface/accelerate)
- datasets: [different repo](https://github.com/huggingface/datasets)
- diffusers: [different repo](https://github.com/huggingface/diffusers)
- rust tokenizers: [different repo](https://github.com/huggingface/tokenizers)

Maintained examples (not research project or legacy):

- Flax: @sanchit-gandhi
- PyTorch: See Models above and tag the person corresponding to the modality of the example.
- TensorFlow: @Rocketknight1

 -->


Comments:
Hello @muellerzr, thanks for the review!

Sorry for the delay, been juggling a few different projects. I'll save some time this week to tackle your comments :)

The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/transformers/pr_29562). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

Updated the PR according to you comments and answered the one about apex.

Gentle ping @Thytu 🤗 

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.

Please note that issues that do not follow the [contributing guidelines](https://github.com/huggingface/transformers/blob/main/CONTRIBUTING.md) are likely to be ignored.