Cleanup deprecated errors

[chilagrow]

Description

While I'm looking at deprecated errors, I've moved them from common to commonerrors.

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 #2411 (d4a879e) into main (3530ddf) will decrease coverage by 37.14%.
The diff coverage is 0.00%.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #2411       +/-   ##
===========================================
- Coverage   63.98%   26.84%   -37.14%     
===========================================
  Files         391      391               
  Lines       18987    19144      +157     
===========================================
- Hits        12148     5139     -7009     
- Misses       5931    13451     +7520     
+ Partials      908      554      -354     

Impacted Files	Coverage Δ
internal/clientconn/conn.go	0.00% <0.00%> (-45.72%)	⬇️
internal/handlers/common/distinct.go	0.00% <0.00%> (-60.76%)	⬇️
internal/handlers/common/filter.go	0.00% <0.00%> (-85.20%)	⬇️
internal/handlers/common/find.go	0.00% <0.00%> (-65.52%)	⬇️
internal/handlers/common/findandmodify.go	0.00% <0.00%> (-78.77%)	⬇️
internal/handlers/common/msg_debugerror.go	0.00% <0.00%> (ø)
internal/handlers/common/params.go	2.93% <0.00%> (-94.04%)	⬇️
internal/handlers/common/projection.go	0.00% <0.00%> (-31.90%)	⬇️
internal/handlers/common/saslstart.go	0.00% <0.00%> (-55.89%)	⬇️
internal/handlers/common/setfreemonitoring.go	0.00% <0.00%> (-60.87%)	⬇️
... and 27 more

... and 102 files with indirect coverage changes

Flag	Coverage Δ
integration	4.75% <0.00%> (-52.13%)	⬇️
mongodb	4.75% <0.00%> (-0.04%)	⬇️
pg	?
unit	25.49% <0.00%> (-0.40%)	⬇️

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

[rumyantseva]

Awesome! I'm glad we finally did it!