Add CI configuration for SQLite without pushdown

[AlekSi]

Description

Refs #3126.

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 #3381 (bdc1ee1) into main (8a2a098) will increase coverage by 0.02%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##             main    #3381      +/-   ##
==========================================
+ Coverage   74.15%   74.18%   +0.02%     
==========================================
  Files         414      414              
  Lines       25330    25330              
==========================================
+ Hits        18784    18790       +6     
+ Misses       5451     5447       -4     
+ Partials     1095     1093       -2     

Flag	Coverage Δ
hana-1	?
hana-2	?
hana-3	?
integration	71.13% <ø> (+0.02%)	⬆️
mongodb-1	4.72% <ø> (ø)
pg-1	43.75% <ø> (+0.03%)	⬆️
pg-2	43.48% <ø> (ø)
pg-3	43.99% <ø> (+0.06%)	⬆️
pushdown-false	56.30% <ø> (?)
pushdown-true	71.09% <ø> (?)
sqlite-1	42.66% <ø> (+<0.01%)	⬆️
sqlite-2	42.11% <ø> (ø)
sqlite-3	43.06% <ø> (ø)
unit	23.31% <ø> (-0.04%)	⬇️

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

[chilagrow]

Great!