test(telemetry): run background health checks with a test delay

Retain the two-minute production constant and extract the same background runner with an explicit test-only delay argument. Correct the startup non-blocking regression after exact-source proof found its invalid constant assignment.

Contract-Neutral: Extract the unchanged telemetry background runner for deterministic testing; production scheduling, payload and privacy contracts are unchanged.
Change-source: pulse-maintainer

internal/telemetry/service_health_test.go

@@ -221,18 +221,16 @@ func TestServiceHealthFailureCategoriesSerializeAndPersist(t *testing.T) {
 }
 
 func TestTelemetryStartDoesNotWaitForServiceHealth(t *testing.T) {
-	originalDelay := startupDelay
-	startupDelay = 0
-	defer func() { startupDelay = originalDelay }()
 	ctx, cancel := context.WithCancel(context.Background())
 	entered, release, started := make(chan struct{}), make(chan struct{}), make(chan struct{})
+	dir := t.TempDir()
 	t.Cleanup(func() { close(release); cancel(); Stop() })
 	go func() {
-		Start(ctx, Config{Enabled: true, Version: "6.4.6", DataDir: t.TempDir(), GetServiceHealth: func() ServiceHealthObservation {
+		startWithDelay(ctx, Config{Enabled: true, Version: "6.4.6", DataDir: dir, GetServiceHealth: func() ServiceHealthObservation {
 			close(entered)
 			<-release
 			return ServiceHealthObservation{Observed: true, Healthy: true}
-		}})
+		}}, 0)
 		close(started)
 	}()
 	select {

internal/telemetry/telemetry.go

@@ -1125,6 +1125,12 @@ var (
 //
 // This is a no-op when outbound usage telemetry is disabled.
 func Start(ctx context.Context, cfg Config) {
+	startWithDelay(ctx, cfg, startupDelay)
+}
+
+// Keep the production settling delay constant while allowing deterministic
+// tests to exercise the same background runner without a two-minute sleep.
+func startWithDelay(ctx context.Context, cfg Config, initialDelay time.Duration) {
 	if !cfg.Enabled {
 		log.Info().Msg("Outbound usage telemetry is disabled (enable via PULSE_TELEMETRY=true or Settings → System)")
 		return
@@ -1154,7 +1160,7 @@ func Start(ctx context.Context, cfg Config) {
 		defer r.wg.Done()
 
 		// Wait for the monitor to connect and populate state before the first ping.
-		startTimer := time.NewTimer(startupDelay)
+		startTimer := time.NewTimer(initialDelay)
 		select {
 		case <-ctx.Done():
 			startTimer.Stop()