[3.12] gh-91054: make code watcher tests resilient to other watchers (GH-107821) (#107835)

gh-91054: make code watcher tests resilient to other watchers (GH-107821)
(cherry picked from commit 2ec16fed14aae896e38dd5bd9e73e2eddc974439)

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