maxTimeMS propagation tests run

[noisersup]

Description

Closes #2983.

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

All modified and coverable lines are covered by tests ✅

Comparison is base (38fb5e4) 74.06% compared to head (733a391) 74.02%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3939      +/-   ##
==========================================
- Coverage   74.06%   74.02%   -0.05%     
==========================================
  Files         330      330              
  Lines       25944    25944              
==========================================
- Hits        19215    19204      -11     
- Misses       5589     5597       +8     
- Partials     1140     1143       +3     

see 4 files with indirect coverage changes

Flag	Coverage Δ
filter-true	70.65% <ø> (-0.05%)	⬇️
hana-1	?
integration	70.65% <ø> (-0.05%)	⬇️
mongodb-1	5.18% <ø> (+0.01%)	⬆️
postgresql-1	49.51% <ø> (-0.11%)	⬇️
postgresql-2	52.16% <ø> (-0.03%)	⬇️
postgresql-3	50.89% <ø> (-0.02%)	⬇️
sqlite-1	48.79% <ø> (ø)
sqlite-2	51.24% <ø> (-0.04%)	⬇️
sqlite-3	49.99% <ø> (-0.10%)	⬇️
unit	30.70% <ø> (ø)

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