Add tests for $$ROOT

[chilagrow]

Description

Closes #1992.

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 #3187 (f56d4eb) into main (74844b1) will increase coverage by 3.88%.
The diff coverage is n/a.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3187      +/-   ##
==========================================
+ Coverage   70.95%   74.84%   +3.88%     
==========================================
  Files         396      396              
  Lines       22210    22210              
==========================================
+ Hits        15760    16623     +863     
+ Misses       5392     4609     -783     
+ Partials     1058      978      -80     

see 74 files with indirect coverage changes

Flag	Coverage Δ
integration	71.23% <ø> (+4.45%)	⬆️
mongodb	5.30% <ø> (ø)
pg	65.21% <ø> (+4.81%)	⬆️
shard-1	55.88% <ø> (-0.65%)	⬇️
shard-2	54.79% <ø> (?)
shard-3	55.12% <ø> (-0.80%)	⬇️
sqlite	33.15% <ø> (-1.91%)	⬇️
unit	24.51% <ø> (-0.16%)	⬇️

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

[rumyantseva]

Great! Thanks for the additional examples!

[noisersup]

LGTM