Run linters on integration tests folder

[ravilushqa]

Description

This PR closes #557 .

Run linters for integration folder

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 3, 2022 at 2:36PM (UTC)

[codecov]

Codecov Report

Merging #1200 (1670111) into main (308fdda) will decrease coverage by 0.14%.
The diff coverage is 66.66%.

❗ Current head 1670111 differs from pull request most recent head 9f61203. Consider uploading reports for the commit 9f61203 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1200      +/-   ##
==========================================
- Coverage   66.46%   66.32%   -0.15%     
==========================================
  Files         251      251              
  Lines       12296    12299       +3     
==========================================
- Hits         8173     8157      -16     
- Misses       3233     3249      +16     
- Partials      890      893       +3     

Impacted Files	Coverage Δ
integration/setup/setup.go	86.40% <0.00%> (-0.85%)	⬇️
integration/setup/common.go	91.12% <66.66%> (ø)
internal/handlers/tigris/msg_datasize.go	65.38% <100.00%> (+0.67%)	⬆️
internal/handlers/tigris/msg_dbstats.go	74.24% <100.00%> (+0.39%)	⬆️
internal/util/version/version.go	55.00% <0.00%> (-5.00%)	⬇️
internal/handlers/pg/pgdb/settings.go	39.53% <0.00%> (-4.66%)	⬇️
internal/handlers/common/filter.go	86.58% <0.00%> (-0.95%)	⬇️

Flag	Coverage Δ
integration	62.59% <66.66%> (-0.15%)	⬇️
mongodb	14.84% <33.33%> (-0.05%)	⬇️
pg	51.83% <33.33%> (-0.16%)	⬇️
tigris	34.67% <50.00%> (-0.02%)	⬇️
unit	23.97% <0.00%> (-0.11%)	⬇️

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[ravilushqa]

@AlekSi can you please have a look at CI. for some reason upload coverage information failing

[AlekSi]

codecov/feedback#126

[AlekSi]

Thank you!