Return correct response if unique index violation happened on SQLite backend

[rumyantseva]

Description

Closes #3183.

The approach with WriteError is the same as in msg_insert for consistency purposes.

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

Merging #3353 (3a95662) into main (481bc96) will increase coverage by 0.07%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #3353      +/-   ##
==========================================
+ Coverage   74.03%   74.11%   +0.07%     
==========================================
  Files         413      413              
  Lines       25292    25305      +13     
==========================================
+ Hits        18726    18755      +29     
+ Misses       5475     5465      -10     
+ Partials     1091     1085       -6     

Files Changed	Coverage
internal/handlers/sqlite/msg_update.go	100.00%

Flag	Coverage Δ
hana-1	?
hana-2	?
hana-3	?
integration	71.14% <100.00%> (+0.06%)	⬆️
mongodb-1	4.73% <0.00%> (-0.01%)	⬇️
pg-1	44.57% <0.00%> (-0.02%)	⬇️
pg-2	44.74% <0.00%> (-0.03%)	⬇️
pg-3	42.31% <0.00%> (-0.03%)	⬇️
sqlite-1	43.13% <100.00%> (-0.06%)	⬇️
sqlite-2	43.57% <33.33%> (+0.02%)	⬆️
sqlite-3	41.22% <33.33%> (-0.01%)	⬇️
unit	23.03% <0.00%> (-0.02%)	⬇️

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

[noisersup]

LGTM