Move old bson package

[AlekSi]

Description

More clean-ups.

Readiness checklist

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

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 68.21%. Comparing base (8483f04) to head (ba12b0d).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4177      +/-   ##
==========================================
- Coverage   74.51%   68.21%   -6.30%     
==========================================
  Files         339      339              
  Lines       22786    22786              
==========================================
- Hits        16978    15544    -1434     
- Misses       4502     5884    +1382     
- Partials     1306     1358      +52     

Files	Coverage Δ
internal/bson2/oldbson/array.go	70.45% <ø> (ø)
internal/bson2/oldbson/binary.go	62.06% <ø> (ø)
internal/bson2/oldbson/bool.go	64.00% <ø> (ø)
internal/bson2/oldbson/cstring.go	73.68% <ø> (ø)
internal/bson2/oldbson/datetime.go	68.18% <ø> (ø)
internal/bson2/oldbson/document.go	58.94% <ø> (ø)
internal/bson2/oldbson/double.go	73.68% <ø> (ø)
internal/bson2/oldbson/int32.go	70.58% <ø> (ø)
internal/bson2/oldbson/int64.go	70.58% <ø> (ø)
internal/bson2/oldbson/null.go	0.00% <ø> (ø)
... and 6 more

... and 66 files with indirect coverage changes

Flag	Coverage Δ
filter-true	60.94% <ø> (-7.12%)	⬇️
hana-1	?
integration	60.94% <ø> (-7.12%)	⬇️
mongodb-1	4.89% <ø> (+<0.01%)	⬆️
postgresql-1	46.58% <ø> (-0.03%)	⬇️
postgresql-2	49.45% <ø> (+0.08%)	⬆️
postgresql-3	?
sqlite-1	?
sqlite-2	48.61% <ø> (+0.07%)	⬆️
sqlite-3	?
unit	32.54% <ø> (ø)

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

[rumyantseva]