gh-117688: Fix deadlock in test_no_stale_references with GIL disabled (#117720)

Check `my_object_collected.wait()` in a loop to give the main thread a
chance to merge the reference count fields. Additionally, call
`my_object_collected.set()` in a background thread to avoid deadlocking
when the destructor is called asynchronously via the eval breaker
within the body of of `my_object_collected.wait()`.