Do not mark released binaries as dirty

[AlekSi]

Description

Closes #2368.

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), Assignee, Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[codecov]

Codecov Report

Merging #2371 (41f8a82) into main (972391d) will decrease coverage by 36.94%.
The diff coverage is n/a.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #2371       +/-   ##
===========================================
- Coverage   63.99%   27.06%   -36.94%     
===========================================
  Files         391      391               
  Lines       18987    18987               
===========================================
- Hits        12151     5139     -7012     
- Misses       5929    13294     +7365     
+ Partials      907      554      -353     

see 125 files with indirect coverage changes

Flag	Coverage Δ
integration	4.79% <ø> (-52.11%)	⬇️
mongodb	4.79% <ø> (ø)
pg	?
unit	25.71% <ø> (-0.18%)	⬇️

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