Fix logging logic when in_order is set to True

[yuxinyuan]

What does this PR do?

This PR fix the logging logic when in_order is set to True. Right now, the in_order flag either hangs the program when main_process_only is also set to True, or does nothing when main_process_only is set to False.

A simple code snippet to test (run with accelerate launch --num_processes=2 test.py):

from accelerate import PartialState
from accelerate.logging import get_logger


s = PartialState()

logger = get_logger("accelerate")
in_order = True
main_process_only = False  # True

logger.info(f"[{s.process_index}] Hello, world!", in_order=in_order, main_process_only=main_process_only)
logger.warning(f"[{s.process_index}] Hello, world!", in_order=in_order, main_process_only=main_process_only)
logger.error(f"[{s.process_index}] Hello, world!", in_order=in_order, main_process_only=main_process_only)

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• This PR fixes a typo or improves the docs (you can dismiss the other checks if that's the case).
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• Did you write any new necessary tests?

Who can review?

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[HuggingFaceDocBuilderDev]

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[BenjaminBossan]

CI is failing because of the str | None type annotation. This syntax has only been added in Python 3.10 but 3.9 is tested. Either you have to use Optional or from __future__ import annotations.

[yuxinyuan]

@BenjaminBossan
Done.

[muellerzr]

Thanks! Overall this looks good to me, however there's logger-related tests which are now failing. Can you modify those tests since our logs differ a bit now?