test(app): internal/app unit tests use 8–17 s of the 15 s budget, time out under load #617

Area: test — unit-test budget · found while building #613

Issue: go test ./internal/app/ takes 8.3–17.0 s on an idle machine (measured in three environments on 2026-09-24: 8.3–17.0 s on main's discovery.go, ~9.4 s on mq-tenant-streams, 10.4 s on main), against the unit-test runner's -timeout 15s. Under load it times out: make ci failed at least five times that evening under heavy load, including TestNew_VerifierPerTenant blocked in os.WriteFile inside the writeSettings helper. Each failure passed when re-run alone. On #612's branch, internal/mq measured ~20 s under load (inferred to be close to the budget when idle, not timed).

Expected: unit packages finish well within the 15 s budget, so make ci does not fail on packages a change never touched.

Scope: profile internal/app tests (boot-per-test cost, settings-directory writes, fixed sleeps/tickers), cut the per-test cost or split the slow ones behind the integration tag; re-time internal/mq after #612.

Related: #613, #612.