Add Kubernetes probes stubs

[noisersup]

Description

Closes #4306.

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.

[rumyantseva]

Looks good for the beginning!

[codecov]

Codecov Report

Attention: Patch coverage is 73.52941% with 9 lines in your changes missing coverage. Please review.

Project coverage is 73.91%. Comparing base (e1258e3) to head (53cdf28).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4378      +/-   ##
==========================================
- Coverage   73.94%   73.91%   -0.03%     
==========================================
  Files         323      323              
  Lines       22364    22398      +34     
==========================================
+ Hits        16537    16556      +19     
- Misses       4615     4623       +8     
- Partials     1212     1219       +7     

Files	Coverage Δ
internal/util/debug/debug.go	81.52% <73.52%> (-4.69%)	⬇️

... and 4 files with indirect coverage changes

Flag	Coverage Δ
filter-true	67.35% <73.52%> (-0.02%)	⬇️
hana-1	?
integration	67.35% <73.52%> (-0.02%)	⬇️
mongodb-1	5.05% <73.52%> (+0.09%)	⬆️
postgresql-1	43.94% <73.52%> (+0.06%)	⬆️
postgresql-2	44.95% <73.52%> (-0.02%)	⬇️
postgresql-3	42.99% <73.52%> (+0.03%)	⬆️
postgresql-4	40.27% <73.52%> (+0.04%)	⬆️
postgresql-5	43.69% <73.52%> (+<0.01%)	⬆️
sqlite-1	43.12% <73.52%> (+0.01%)	⬆️
sqlite-2	?
sqlite-3	42.22% <73.52%> (+0.07%)	⬆️
sqlite-4	39.42% <73.52%> (+0.05%)	⬆️
sqlite-5	43.04% <73.52%> (+<0.01%)	⬆️
unit	33.04% <0.00%> (-0.06%)	⬇️

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

[noisersup]

@rumyantseva PTAL, I've removed one TODO comment, as I believe that's what we expect from liveness implementation.

[rumyantseva]

Ok, I tried it locally :)
Looks good!