BUG: Fix bug with logging and n_jobs>1

[larsoner]

cc @hoechenberger I can replicate -- locally the added test passes with n_jobs=1 and fails when n_jobs=2:

mne/utils/tests/test_logging.py:276: in test_verbose_threads
    assert out == want_levels
E   assert [20, 20, 20, 20, 20] == [30, 30, 30, 30, 30]
E     At index 0 diff: 20 != 30
E     Use -v to get more diff

So somehow we need to get the logger.level inside the parallel_func'ed function to persist. Not sure what it'll take but I'll try to look at some point

[larsoner]

@hoechenberger I can replicate your issue in MNE-BIDS-Pipeline on mne main with:

$ MNE_LOGGING_LEVEL=info pytest mne_bids_pipeline -k ds001810
=============================================================================== test session starts ================================================================================
platform linux -- Python 3.11.4, pytest-7.4.0, pluggy-1.0.0 -- /home/larsoner/python/virtualenvs/base/bin/python3
...
┌────────┬ preprocessing/_01_data_quality ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
│16:45:45│ ⏳️ sub-01 ses-anodalpost Initializing report HDF5 file
│16:45:45│ ⏳️ sub-01 ses-anodalpre Initializing report HDF5 file
Saving report to : /home/larsoner/mne_data/derivatives/mne-bids-pipeline/ds001810/sub-01/ses-anodalpre/eeg/sub-01_ses-anodalpre_task-attentionalblink_report.h5
Saving report to : /home/larsoner/mne_data/derivatives/mne-bids-pipeline/ds001810/sub-01/ses-anodalpost/eeg/sub-01_ses-anodalpost_task-attentionalblink_report.h5
Embedding : jquery-3.6.0.min.js
Embedding : bootstrap.bundle.min.js
Embedding : bootstrap.min.css
Embedding : bootstrap-table/bootstrap-table.min.js
Embedding : bootstrap-table/bootstrap-table.min.css

And on this PR I get the same thing, as I need to port the change over to MNE-BIDS-Pipeline. But making the change there I get:

$ MNE_LOGGING_LEVEL=info pytest mne_bids_pipeline -k ds001810
=============================================================================== test session starts ================================================================================
platform linux -- Python 3.11.4, pytest-7.4.0, pluggy-1.0.0 -- /home/larsoner/python/virtualenvs/base/bin/python3
...
┌────────┬ preprocessing/_01_data_quality ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
│16:50:18│ ⏳️ sub-01 ses-anodalpre Adding original raw data to report
│16:50:18│ ⏳️ sub-01 ses-cathodalpost Adding original raw data to report
│16:50:18│ ⏳️ sub-01 ses-anodalpost Adding original raw data to report
│16:50:18│ ⏳️ sub-01 ses-anodaltDCS Adding original raw data to report
...

[hoechenberger]

This looks good to me!

[hoechenberger]

Care to add a changelog entry?