Deadlock - Ensure resumed flight tasks are still fetched

[fjetter]

This is another deadlock introduced by #5160. In a nutshell, all tasks entering gather_deps must be handled / transitioned out of flight even though we're not trying to fetch all of the keys.

A second problem popping up is that the TaskState.done was not properly (re-)set causing dependencies to be fetched to be transitioned falsely.

This also closes #5406

Follow up PR to establish an enum as the worker task state name: #5444

[fjetter]

FWIW the power user who originally reported this issue tried this PR and it looks promising to not deadlock any longer.

[crusaderky]

cosmetic tweaks

[fjetter]

I see distributed/tests/test_steal.py::test_reschedule_concurrent_requests_deadlock still timing out, e.g. https://github.com/dask/distributed/pull/5444/checks?check_run_id=3953535224

couldn't reproduce, yet

[jrbourbeau]

Thanks @fjetter