Minor handlers refactoring

[AlekSi]

Description

Do old TODO.

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 15, 2022 at 3:12PM (UTC)

[codecov]

Codecov Report

Merging #1264 (9e0fffd) into main (b45db81) will decrease coverage by 0.14%.
The diff coverage is 86.95%.

❗ Current head 9e0fffd differs from pull request most recent head 254e39f. Consider uploading reports for the commit 254e39f to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1264      +/-   ##
==========================================
- Coverage   66.56%   66.41%   -0.15%     
==========================================
  Files         269      269              
  Lines       12575    12574       -1     
==========================================
- Hits         8370     8351      -19     
- Misses       3304     3316      +12     
- Partials      901      907       +6     

Impacted Files	Coverage Δ
internal/handlers/pg/msg_createindexes.go	0.00% <0.00%> (ø)
internal/handlers/pg/msg_explain.go	0.00% <0.00%> (ø)
internal/handlers/pg/msg_hello.go	76.00% <0.00%> (ø)
internal/handlers/pg/msg_ismaster.go	76.00% <0.00%> (ø)
internal/handlers/pg/msg_ping.go	57.14% <0.00%> (ø)
internal/handlers/pg/msg_collstats.go	57.14% <100.00%> (ø)
internal/handlers/pg/msg_count.go	48.27% <100.00%> (ø)
internal/handlers/pg/msg_create.go	79.41% <100.00%> (ø)
internal/handlers/pg/msg_datasize.go	58.82% <100.00%> (ø)
internal/handlers/pg/msg_dbstats.go	65.11% <100.00%> (ø)
... and 15 more

Flag	Coverage Δ
integration	62.66% <86.95%> (-0.15%)	⬇️
mongodb	14.16% <8.69%> (-0.05%)	⬇️
pg	52.17% <86.95%> (-0.15%)	⬇️
tigris	33.85% <0.00%> (-0.03%)	⬇️
unit	24.79% <2.17%> (-0.04%)	⬇️

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[AlekSi]

Hm……