Improve tests cleanup

[AlekSi]

Description

That should make tests more stable.

Readiness checklist

• I added tests for new functionality or bugfixes.
• I ran task all, and it passed.
• I added/updated comments for both exported and unexported top-level declarations (functions, types, etc).
• I checked comments rendering with task godocs.
• I ensured that the title is good enough for the changelog.
• (for maintainers only) I set Reviewers (@FerretDB/core), Assignee, Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[vercel]

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Name	Status	Preview	Updated
ferret-db	✅ Ready (Inspect)	Visit Preview	Oct 19, 2022 at 2:03PM (UTC)

[rumyantseva]

LGTM

[codecov]

Codecov Report

Merging #1287 (df6bb13) into main (a51aa2d) will decrease coverage by 0.08%.
The diff coverage is 100.00%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1287      +/-   ##
==========================================
- Coverage   67.16%   67.07%   -0.09%     
==========================================
  Files         270      271       +1     
  Lines       12722    12730       +8     
==========================================
- Hits         8545     8539       -6     
- Misses       3275     3284       +9     
- Partials      902      907       +5     

Impacted Files	Coverage Δ
internal/util/testutil/testutil.go	100.00% <100.00%> (ø)
internal/util/testutil/testutil_unix.go	100.00% <100.00%> (ø)
internal/clientconn/conninfo/conn_info.go	66.66% <0.00%> (-16.67%)	⬇️
internal/util/version/version.go	48.52% <0.00%> (-4.42%)	⬇️
internal/handlers/common/filter.go	86.58% <0.00%> (-0.95%)	⬇️

Flag	Coverage Δ
integration	62.99% <100.00%> (-0.08%)	⬇️
mongodb	14.13% <100.00%> (+0.03%)	⬆️
pg	52.41% <100.00%> (-0.07%)	⬇️
tigris	34.10% <100.00%> (+0.01%)	⬆️
unit	25.10% <100.00%> (+<0.01%)	⬆️

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