[3.12] gh-91051: fix type watcher test to be robust to existing watcher (GH-107989) (#108053)

gh-91051: fix type watcher test to be robust to existing watcher (GH-107989)
(cherry picked from commit fce93c80ae2d792b8ca443b044e28abbf28bb89a)

Co-authored-by: Carl Meyer <carl@oddbird.net>