cleanup: rename logging option

[dbolduc]

Part of the work for #14269

I am not sure whether I should call this a cleanup or a feat. :shrug:

env var changes will come later.

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Testing

I did run builds before making the second commit of this PR. If people think we would have more confidence in the code if we

1. introduce the option in one PR
2. update our usage of the option in a second PR

... just say the words.

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This change is 

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 93.22034% with 4 lines in your changes are missing coverage. Please review.

Project coverage is 93.24%. Comparing base (d5a4ed5) to head (736d275).

Files	Patch %	Lines
...y/v2/minimal/internal/dataset_rest_stub_factory.cc	50.00%	1 Missing :warning:
...query/v2/minimal/internal/job_rest_stub_factory.cc	50.00%	1 Missing :warning:
...y/v2/minimal/internal/project_rest_stub_factory.cc	50.00%	1 Missing :warning:
...ery/v2/minimal/internal/table_rest_stub_factory.cc	50.00%	1 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #14271      +/-   ##
==========================================
- Coverage   93.50%   93.24%   -0.27%     
==========================================
  Files        2135     2214      +79     
  Lines      191691   193535    +1844     
==========================================
+ Hits       179238   180459    +1221     
- Misses      12453    13076     +623     

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