Use single transaction per msg_insert request

[rumyantseva]

Description

This PR refs #1203.

This PR didn't fix the tests, but I consider it an improvement, so please review.

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 5, 2022 at 10:40AM (UTC)

[codecov]

Codecov Report

Merging #1213 (d7000e1) into main (c349a2b) will increase coverage by 0.06%.
The diff coverage is 50.00%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1213      +/-   ##
==========================================
+ Coverage   66.39%   66.45%   +0.06%     
==========================================
  Files         252      252              
  Lines       12324    12331       +7     
==========================================
+ Hits         8182     8195      +13     
+ Misses       3250     3243       -7     
- Partials      892      893       +1     

Impacted Files	Coverage Δ
internal/handlers/pg/msg_update.go	57.55% <0.00%> (ø)
internal/handlers/pg/msg_insert.go	41.42% <43.47%> (+2.03%)	⬆️
internal/handlers/pg/msg_findandmodify.go	73.21% <100.00%> (+0.36%)	⬆️
internal/util/version/version.go	55.00% <0.00%> (-5.00%)	⬇️
internal/handlers/common/filter.go	86.58% <0.00%> (ø)
internal/handlers/pg/pgdb/query.go	43.44% <0.00%> (+2.75%)	⬆️
internal/handlers/pg/pgdb/settings.go	44.18% <0.00%> (+4.65%)	⬆️

Flag	Coverage Δ
integration	62.70% <50.00%> (+0.03%)	⬆️
mongodb	14.82% <0.00%> (-0.02%)	⬇️
pg	51.84% <50.00%> (+0.04%)	⬆️
tigris	34.86% <0.00%> (-0.05%)	⬇️
unit	24.12% <0.00%> (+0.07%)	⬆️

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[AlekSi]

Please mark this PR as ready for review when ready