Improve bson2 and wire logging

[AlekSi]

Description

Closes #3759.

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

Attention: Patch coverage is 67.41214% with 102 lines in your changes are missing coverage. Please review.

Project coverage is 73.77%. Comparing base (f460194) to head (959ea3f).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4148      +/-   ##
==========================================
- Coverage   74.67%   73.77%   -0.90%     
==========================================
  Files         353      354       +1     
  Lines       22797    23012     +215     
==========================================
- Hits        17024    16978      -46     
- Misses       4481     4738     +257     
- Partials     1292     1296       +4     

Files	Coverage Δ
internal/bson2/bson2.go	84.37% <ø> (ø)
internal/bson2/raw_document.go	84.00% <100.00%> (+0.43%)	⬆️
internal/util/testutil/dump.go	54.28% <100.00%> (+27.01%)	⬆️
internal/bson2/document.go	62.85% <60.00%> (+11.38%)	⬆️
internal/wire/op_reply.go	57.14% <81.81%> (+0.69%)	⬆️
internal/bson2/raw_array.go	30.30% <0.00%> (-1.96%)	⬇️
internal/wire/op_query.go	50.00% <69.23%> (+0.61%)	⬆️
internal/bson2/array.go	63.15% <64.70%> (+0.65%)	⬆️
internal/bson2/logging.go	92.64% <92.64%> (ø)
internal/wire/op_msg.go	63.27% <52.63%> (-4.52%)	⬇️
... and 1 more

... and 31 files with indirect coverage changes

Flag	Coverage Δ
filter-false	?
filter-true	66.77% <50.82%> (-1.70%)	⬇️
hana-1	?
integration	66.77% <50.82%> (-1.73%)	⬇️
mongodb-1	4.85% <0.00%> (-0.04%)	⬇️
mysql-1	?
mysql-2	?
mysql-3	?
postgresql-1	48.11% <50.82%> (-0.42%)	⬇️
postgresql-2	46.94% <50.00%> (-0.41%)	⬇️
postgresql-3	49.24% <50.82%> (-0.43%)	⬇️
sqlite-1	47.25% <50.82%> (-0.37%)	⬇️
sqlite-2	46.08% <50.00%> (-0.43%)	⬇️
sqlite-3	48.41% <50.82%> (-0.43%)	⬇️
unit	32.84% <67.41%> (+0.36%)	⬆️

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

[chilagrow]

The log format is easy to read 🤗

[AlekSi]

TestCheckingNestedDocuments fails hard, and the test itself is broken