Add basic metrics, logging and tracing for SQLite

[AlekSi]

Description

More will be added later.

Closes #2909.

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

[codecov]

Codecov Report

Merging #3123 (fecdf52) into main (a398e31) will decrease coverage by 0.14%.
The diff coverage is 55.41%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3123      +/-   ##
==========================================
- Coverage   75.94%   75.81%   -0.14%     
==========================================
  Files         391      392       +1     
  Lines       21596    21705     +109     
==========================================
+ Hits        16401    16455      +54     
- Misses       4240     4297      +57     
+ Partials      955      953       -2     

Files Changed	Coverage Δ
internal/backends/backend.go	90.69% <0.00%> (-9.31%)	⬇️
internal/handlers/sqlite/sqlite.go	66.66% <0.00%> (-5.34%)	⬇️
internal/util/fsql/metrics.go	15.90% <15.90%> (ø)
internal/backends/sqlite/backend.go	77.41% <20.00%> (-11.47%)	⬇️
internal/backends/sqlite/metadata/registry.go	68.46% <42.85%> (+1.00%)	⬆️
internal/backends/sqlite/metadata/pool/pool.go	74.04% <48.64%> (-10.72%)	⬇️
internal/backends/sqlite/collection.go	62.23% <100.00%> (ø)
internal/util/fsql/db.go	100.00% <100.00%> (ø)

Flag	Coverage Δ
hana	?
integration	72.36% <55.41%> (-0.12%)	⬇️
mongodb	5.44% <0.00%> (-0.03%)	⬇️
pg	65.65% <0.00%> (-0.34%)	⬇️
shard-1	55.52% <55.41%> (-0.04%)	⬇️
shard-2	53.57% <55.41%> (-0.06%)	⬇️
shard-3	52.65% <0.00%> (-0.27%)	⬇️
sqlite	41.58% <55.41%> (+0.04%)	⬆️
unit	23.84% <24.20%> (-0.09%)	⬇️

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

[chilagrow]

Looks great 🚀

[rumyantseva]

LGTM!