Fix tests for MongoDB with enabled replica set

[rumyantseva]

Description

Closes #3310.

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

Merging #3604 (1cd38d5) into main (d743808) will decrease coverage by 6.19%.
The diff coverage is n/a.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3604      +/-   ##
==========================================
- Coverage   76.82%   70.63%   -6.19%     
==========================================
  Files         323      323              
  Lines       23029    23029              
==========================================
- Hits        17692    16267    -1425     
- Misses       4311     5652    +1341     
- Partials     1026     1110      +84     

see 67 files with indirect coverage changes

Flag	Coverage Δ
filter-false	?
filter-true	66.24% <ø> (-6.68%)	⬇️
hana-1	?
integration	66.24% <ø> (-6.71%)	⬇️
mongodb-1	5.46% <ø> (-0.01%)	⬇️
postgresql-1	?
postgresql-2	51.63% <ø> (-0.28%)	⬇️
postgresql-3	50.69% <ø> (-0.24%)	⬇️
sort-false	66.24% <ø> (-6.24%)	⬇️
sort-true	?
sqlite-1	?
sqlite-2	50.90% <ø> (-0.22%)	⬇️
sqlite-3	49.90% <ø> (-0.26%)	⬇️
unit	30.08% <ø> (ø)

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

[noisersup]

Looks good to me!