Relax PostgreSQL connection checks

[AlekSi]

Description

Allow more locales, improve error messages and documentation.

Readiness checklist

• I added/updated unit tests.
• I added/updated integration/compatibility tests.
• 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), Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[codecov]

Codecov Report

Merging #2602 (469de7c) into main (136df12) will increase coverage by 38.53%.
The diff coverage is 78.57%.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #2602       +/-   ##
===========================================
+ Coverage   27.20%   65.74%   +38.53%     
===========================================
  Files         414      414               
  Lines       20366    20383       +17     
===========================================
+ Hits         5540    13400     +7860     
+ Misses      14248     6032     -8216     
- Partials      578      951      +373     

Impacted Files	Coverage Δ
internal/handlers/registry/hana.go	8.33% <0.00%> (-1.67%)	⬇️
internal/handlers/registry/tigris.go	5.00% <0.00%> (-0.56%)	⬇️
internal/handlers/pg/pg.go	79.10% <50.00%> (+58.20%)	⬆️
internal/handlers/pg/pgdb/pool.go	69.46% <88.88%> (+8.44%)	⬆️

... and 135 files with indirect coverage changes

Flag	Coverage Δ
integration	58.85% <76.19%> (+53.41%)	⬆️
mongodb	5.44% <0.00%> (-0.01%)	⬇️
pg	58.76% <76.19%> (?)
unit	25.69% <76.19%> (+0.12%)	⬆️

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

[rumyantseva]

LGTM, one minor question.

[AlekSi]

@Fashander PTAL