Investigate non-repeatable edx-platform dependencies in tests

[timmc-edx]

The CI GitHub Action uses make test-requirements, which uses pip-sync, so we should be getting repeatable dependency sets even though our test runners re-use their virtualenvs. However, we've been seeing some cases where tests pass on one PR and then fail on another due to issues related to dependencies.

[timmc-edx]

I think the correct approach is just to add pip check to one of our test runners.

We would first need to address #31374 since pip check would currently fail due to make test-requirements not installing django.txt. #31387 is a more sweeping approach to a fix, but would also cover cases where someone manually adjusts a dependency lockfile rather than using make compile-requirements.

However, this work could be done separately. One option would be to add an action that checks that make compile-requirements requirements does not change the output of pip list --format=freeze and passes pip check.

[timmc-edx]

#31387 should address this, but letting it sit for a week before declaring victory (in case it needs to be rolled back, etc.)