Make logger configurable in the embedded ferretdb package

[fadyat]

Description

Closes #4014.

Readiness checklist

• I added/updated unit tests (and they pass).
• I added/updated integration/compatibility tests (and they pass).
• I added/updated comments and checked rendering.
• I made spot refactorings.
• I updated user documentation.
• I ran task all, and it passed.
• I ensured that PR title is good enough for the changelog.
• (for maintainers only) I set Reviewers (@FerretDB/core), Milestone (Next), Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[codecov]

Codecov Report

Attention: 2 lines in your changes are missing coverage. Please review.

Comparison is base (033dfef) 76.36% compared to head (9d59293) 75.11%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4028      +/-   ##
==========================================
- Coverage   76.36%   75.11%   -1.25%     
==========================================
  Files         349      349              
  Lines       22162    22170       +8     
==========================================
- Hits        16925    16654     -271     
- Misses       3933     4250     +317     
+ Partials     1304     1266      -38     

Files	Coverage Δ
internal/bson2/slog.go	87.50% <ø> (ø)
internal/util/logging/logging.go	80.00% <100.00%> (+0.33%)	⬆️
ferretdb/ferretdb.go	86.51% <86.66%> (-1.29%)	⬇️

... and 22 files with indirect coverage changes

Flag	Coverage Δ
filter-false	?
filter-true	67.36% <16.66%> (-1.60%)	⬇️
hana-1	?
integration	67.36% <16.66%> (-1.66%)	⬇️
mongodb-1	4.69% <16.66%> (-0.04%)	⬇️
mysql-1	?
mysql-2	?
mysql-3	?
postgresql-1	49.04% <16.66%> (-0.16%)	⬇️
postgresql-2	48.64% <16.66%> (-0.23%)	⬇️
postgresql-3	48.76% <16.66%> (-0.10%)	⬇️
sqlite-1	48.25% <16.66%> (-0.13%)	⬇️
sqlite-2	47.94% <16.66%> (-0.09%)	⬇️
sqlite-3	47.91% <16.66%> (-0.10%)	⬇️
unit	33.16% <88.88%> (+0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

[noisersup]

Good job! LGTM

[chilagrow]

Thanks for your contribution 🤗