Integration tests

[Felixoid]

Attempt to rearrange integration tests to make them run locally.

Now, they can run as make -C tests/integration test from the repo root.

GHA definition was reduced significantly.

tests/test_crate is used for cargo tests; locally, all tests are finished in around one minute in the case of the second run.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 71.24%. Comparing base (f52f7ce) to head (787e01b).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2564   +/-   ##
=======================================
  Coverage   71.24%   71.24%           
=======================================
  Files          64       64           
  Lines       35622    35622           
=======================================
  Hits        25379    25379           
  Misses      10243    10243           

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