Fix PLAIN mechanism authentication incorrectly working

[chilagrow]

Description

I found a bug related to enforcing new authentication, see added test.

Closes #1877.

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 91.66667% with 2 lines in your changes are missing coverage. Please review.

Project coverage is 73.80%. Comparing base (e98d536) to head (4748386).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4163      +/-   ##
==========================================
- Coverage   74.74%   73.80%   -0.94%     
==========================================
  Files         353      353              
  Lines       22789    22797       +8     
==========================================
- Hits        17034    16826     -208     
- Misses       4470     4692     +222     
+ Partials     1285     1279       -6     

Files	Coverage Δ
internal/backends/mysql/metadata/registry.go	64.13% <100.00%> (-0.95%)	⬇️
internal/backends/postgresql/metadata/registry.go	71.89% <100.00%> (-0.41%)	⬇️
internal/clientconn/conninfo/conn_info.go	96.49% <100.00%> (+0.06%)	⬆️
internal/handler/msg_logout.go	100.00% <100.00%> (ø)
internal/handler/msg_saslstart.go	78.70% <100.00%> (+0.13%)	⬆️
internal/handler/authenticate.go	76.81% <86.66%> (-0.97%)	⬇️

... and 28 files with indirect coverage changes

Flag	Coverage Δ
filter-false	?
filter-true	67.24% <87.50%> (-1.26%)	⬇️
hana-1	?
integration	67.24% <87.50%> (-1.33%)	⬇️
mongodb-1	4.88% <0.00%> (-0.01%)	⬇️
mysql-1	?
mysql-2	?
mysql-3	?
postgresql-1	48.48% <75.00%> (-0.04%)	⬇️
postgresql-2	47.30% <62.50%> (+<0.01%)	⬆️
postgresql-3	49.32% <50.00%> (-0.29%)	⬇️
sqlite-1	47.57% <70.83%> (-0.11%)	⬇️
sqlite-2	46.46% <58.33%> (+0.02%)	⬆️
sqlite-3	48.73% <45.83%> (-0.04%)	⬇️
unit	32.48% <16.66%> (-0.02%)	⬇️

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