Disconnect client in embedded tests

[AlekSi]

Readiness checklist

• I added tests for new functionality or bugfixes.
• I ran task all, and it passed.
• I added/updated comments for both exported and unexported top-level declarations (functions, types, etc).
• I checked comments rendering with task godocs.
• (for maintainers only) I set Reviewers, Assignee, Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[codecov]

Codecov Report

Merging #890 (43df967) into main (b6f00e6) will decrease coverage by 0.01%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #890      +/-   ##
==========================================
- Coverage   59.34%   59.32%   -0.02%     
==========================================
  Files         225      225              
  Lines       10020    10024       +4     
==========================================
+ Hits         5946     5947       +1     
- Misses       3376     3379       +3     
  Partials      698      698              

Impacted Files	Coverage Δ
integration/setup.go	87.40% <100.00%> (+0.09%)	⬆️
internal/clientconn/listener.go	78.72% <100.00%> (+0.70%)	⬆️
internal/util/ctxutil/ctxutil.go	88.23% <0.00%> (-11.77%)	⬇️
internal/util/version/version.go	55.00% <0.00%> (-5.00%)	⬇️
internal/clientconn/conn.go	46.79% <0.00%> (-0.76%)	⬇️
internal/handlers/pg/pgdb/databases.go	59.70% <0.00%> (+5.97%)	⬆️

Flag	Coverage Δ
integration	61.55% <100.00%> (+0.07%)	⬆️
mongodb	18.51% <53.84%> (-0.34%)	⬇️
pg	61.48% <100.00%> (+0.07%)	⬆️
unit	24.65% <0.00%> (-0.02%)	⬇️

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

[rumyantseva]

It's ok'ish that we fix it this way... But!
It feels like our embedded server needs a proper Shutdown to stop gracefully. Simple context propagation is not enough.