…roject (apache#42505)

This is only a partial split so far. It moves all the code and tests, but
leaves the creation of `core/` to a separate PR as this is already large
enough.

In addition to the straight file rename the other changes I had to make here
are:

- Some mypy/typing fixes.

  Mypy can be fragile about what it picks up when, so maybe some of those
  changes were caused by that. But the typing changes aren't large.

- Improve typing in common.sql type stub

  Again, likely a mypy file oddity, but the types should be safe

- Removed the `check-providers-init-file-missing` check

  This isn't needed now that airflow/providers shouldn't exist at all in the
  main tree.

- Create a "dev.tests_common" package that contains helper files and common
  pytest fixtures

  Since the provider tests are no longer under tests/ they don't automatically
  share the fixtures from the parent `tests/conftest.py` so they needed
  extracted.

  Ditto for `tests.test_utils` -- they can't be easily imported in provider
  tests anymore, so they are moved to a more explicit shared location.

In future we should switch how the CI image is built to make better use of UV
caching than our own approach as that would remvoe a lot of custom code.