Remove the need to close conninfo

[AlekSi]

Description

It is a simple object now.

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 #3376 (00f650d) into main (9f8f895) will decrease coverage by 0.10%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #3376      +/-   ##
==========================================
- Coverage   74.20%   74.11%   -0.10%     
==========================================
  Files         413      413              
  Lines       25321    25312       -9     
==========================================
- Hits        18789    18759      -30     
- Misses       5440     5456      +16     
- Partials     1092     1097       +5     

Files Changed	Coverage
internal/clientconn/conn.go	100.00%
internal/clientconn/conninfo/conn_info.go	100.00%

Flag	Coverage Δ
hana-1	?
hana-2	?
hana-3	?
integration	71.05% <100.00%> (-0.11%)	⬇️
mongodb-1	4.72% <0.00%> (+<0.01%)	⬆️
pg-1	43.74% <100.00%> (-0.07%)	⬇️
pg-2	43.51% <100.00%> (-0.03%)	⬇️
pg-3	44.06% <100.00%> (-0.05%)	⬇️
sqlite-1	42.63% <100.00%> (-0.08%)	⬇️
sqlite-2	42.08% <100.00%> (-0.03%)	⬇️
sqlite-3	42.99% <100.00%> (-0.07%)	⬇️
unit	23.27% <20.00%> (+<0.01%)	⬆️

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

[chilagrow]

Looks good to me!

[rumyantseva]