Do not use fjson

[AlekSi]

Description

Closes #4157.

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 44.82759% with 16 lines in your changes are missing coverage. Please review.

Project coverage is 73.86%. Comparing base (c89b88e) to head (4952712).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4175      +/-   ##
==========================================
- Coverage   74.49%   73.86%   -0.63%     
==========================================
  Files         354      353       -1     
  Lines       23038    22985      -53     
==========================================
- Hits        17162    16979     -183     
- Misses       4555     4708     +153     
+ Partials     1321     1298      -23     

Files	Coverage Δ
internal/bson/bson.go	0.00% <ø> (-43.34%)	⬇️
internal/bson2/array.go	65.45% <ø> (+4.43%)	⬆️
internal/bson2/document.go	61.76% <ø> (-2.13%)	⬇️
internal/bson2/logging.go	90.41% <100.00%> (+0.27%)	⬆️
internal/bson2/raw_array.go	32.25% <ø> (+3.68%)	⬆️
internal/bson2/raw_document.go	83.56% <ø> (+1.74%)	⬆️
internal/wire/op_msg.go	70.08% <100.00%> (ø)
internal/wire/op_query.go	53.40% <100.00%> (ø)
internal/wire/op_reply.go	60.86% <100.00%> (ø)
internal/bson2/bson2.go	83.07% <0.00%> (-1.30%)	⬇️
... and 2 more

... and 13 files with indirect coverage changes

Flag	Coverage Δ
filter-true	67.31% <17.24%> (-0.10%)	⬇️
hana-1	?
integration	67.31% <17.24%> (-0.10%)	⬇️
mongodb-1	4.88% <0.00%> (+0.04%)	⬆️
postgresql-1	46.61% <17.24%> (+0.49%)	⬆️
postgresql-2	49.48% <17.24%> (+0.50%)	⬆️
postgresql-3	49.36% <17.24%> (+0.50%)	⬆️
sqlite-1	45.78% <17.24%> (+0.46%)	⬆️
sqlite-2	48.63% <17.24%> (+0.56%)	⬆️
sqlite-3	48.54% <17.24%> (+0.48%)	⬆️
unit	32.93% <44.82%> (-0.05%)	⬇️

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