`Checkdocs` checks issues, separate GitHub code

[kropidlowsky]

Description

Separated GitHub code for checking statuses of issues and added this functionality to Checkdocs. Done some spot refactoring to Checkcomments.

Closes #4171.

Readiness checklist

• [ ] I added/updated unit tests (and they pass).
• [ ] I added/updated integration/compatibility tests (and they pass).
• [x] I added/updated comments and checked rendering.
• [x] I made spot refactorings.
• [ ] I updated user documentation.
• [ ] I ran task all, and it passed.
• [x] I ensured that PR title is good enough for the changelog.
• [ ] (for maintainers only) I set Reviewers (@FerretDB/core), Milestone (Next), Labels, Project and project's Sprint fields.
• [ ] I marked all done items in this checklist.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 73.36%. Comparing base (22c0906) to head (7622cb2).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4258      +/-   ##
==========================================
- Coverage   74.45%   73.36%   -1.10%     
==========================================
  Files         329      329              
  Lines       23067    23067              
==========================================
- Hits        17174    16922     -252     
- Misses       4618     4913     +295     
+ Partials     1275     1232      -43     

see 12 files with indirect coverage changes

Flag	Coverage Δ
filter-true	66.01% <ø> (-1.15%)	:arrow_down:
hana-1	?
integration	66.01% <ø> (-1.15%)	:arrow_down:
mongodb-1	5.34% <ø> (ø)
postgresql-1	42.07% <ø> (+<0.01%)	:arrow_up:
postgresql-2	42.03% <ø> (ø)
postgresql-3	41.88% <ø> (+0.06%)	:arrow_up:
postgresql-4	43.42% <ø> (+0.04%)	:arrow_up:
postgresql-5	44.76% <ø> (+<0.01%)	:arrow_up:
sqlite-1	41.03% <ø> (ø)
sqlite-2	41.17% <ø> (+0.02%)	:arrow_up:
sqlite-3	40.80% <ø> (-0.04%)	:arrow_down:
sqlite-4	42.33% <ø> (ø)
sqlite-5	43.81% <ø> (+0.04%)	:arrow_up:
unit	33.40% <ø> (ø)

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

[mergify[bot]]

@kropidlowsky this pull request has merge conflicts.

[kropidlowsky]

Hi @AlekSi,

In a recent commit, I replaced the short variable declaration with the standard variable declaration for the err variable to comply with the linter's requirements (both locally and on GitHub Action).

However, I've observed that in other Go files, the short variable declaration is being used and accepted by the linter.

[mergify[bot]]

@kropidlowsky this pull request has merge conflicts.