Remove Tigris from tests

[AlekSi]

Description

That's all Folks!

Closes #2253.

Readiness checklist

• I added/updated unit tests.
• I added/updated integration/compatibility tests.
• 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 #3002 (48a7cb5) into main (5ee5a5b) will decrease coverage by 1.60%.
The diff coverage is 100.00%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3002      +/-   ##
==========================================
- Coverage   75.61%   74.02%   -1.60%     
==========================================
  Files         385      385              
  Lines       21060    20959     -101     
==========================================
- Hits        15924    15514     -410     
- Misses       4197     4491     +294     
- Partials      939      954      +15     

Impacted Files	Coverage Δ
integration/helpers.go	84.70% <ø> (+2.23%)	⬆️
integration/setup/test_helpers.go	100.00% <ø> (+7.14%)	⬆️
integration/shareddata/scalars.go	100.00% <ø> (ø)
integration/setup/setup.go	79.77% <100.00%> (+5.68%)	⬆️
integration/setup/setup_compat.go	92.37% <100.00%> (+11.49%)	⬆️
integration/shareddata/provider.go	100.00% <100.00%> (+19.71%)	⬆️
internal/handlers/sqlite/msg_update.go	79.33% <100.00%> (+14.93%)	⬆️

... and 36 files with indirect coverage changes

Flag	Coverage Δ
hana	?
integration	70.35% <100.00%> (-1.76%)	⬇️
mongodb	5.36% <45.45%> (-0.18%)	⬇️
pg	60.45% <54.54%> (-5.56%)	⬇️
shard-1	36.87% <100.00%> (-18.14%)	⬇️
shard-2	56.29% <18.18%> (+5.44%)	⬆️
shard-3	54.82% <54.54%> (-0.45%)	⬇️
sqlite	45.90% <100.00%> (+3.82%)	⬆️
unit	24.39% <0.00%> (-0.01%)	⬇️

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

[rumyantseva]