gh-116631: Fix race condition in `test_shutdown_immediate_put_join` (#116670)

The test case had a race condition: if `q.task_done()` was executed
after `shutdown(immediate=True)`, then it would raise an exception
because the immediate shutdown already emptied the queue. This happened
rarely with the GIL (due to the switching interval), but frequently in
the free-threaded build.
1 file changed