New restores every unfinished task in the shared database and runs its planner, worker and deadline loops on the server context. Tests that passed context.Background() never stopped or joined them, so they kept writing under the manager TempDir after the test returned and the TempDir cleanup failed with directory not empty. Add stopTestServer, which cancels the context, waits for each task to go quiescent, joins its loops, the archive worker and the side-question writer, and defer it right after New in every test that started a live server.
defer m.Close() ran before the t.Cleanup DeleteTask calls, so they raced a closed database and the late writers they trigger could still touch the temp dir while RemoveAll was already walking it (the CI-only TempDir: directory not empty flake). The manager now closes via a t.Cleanup registered first (runs last, LIFO) and the temp dir is removed with a tolerated failure.
BaaRai