Restructure step 0 done: notice table test, flaky-link proxy, liveness on the engine clock, STARSYNC_PROFILE

- notice_table_test: one row per AppEvent variant through noticeFor.
- FlakyProxy (core/testing.dart): pass, blackhole (half-open), delay,
  hold, cut after N bytes, reset; demo tests against today's server.
- Liveness (stale/drop/ping) on the engine clock, so grace can be tested
  with a fake clock; Connection takes an injectable clock.
- AppDirs with STARSYNC_PROFILE=<name>: separate data and logs, so two
  instances run on one machine.
- DEVELOPMENT: scenario list per restructure step; test tags follow the
  new step order.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

packages/server/lib/src/server_hub.dart

@@ -519,7 +519,7 @@ void mountSyncRoute(
         ? '${req.url.host.contains(':') ? '[${req.url.host}]' : req.url.host}:${req.url.port}'
         : (req.url.host.contains(':') ? '[${req.url.host}]' : req.url.host);
     return WebSocketUpgrade((final ws) async {
-      ws.pingInterval = Duration(seconds: RelayConstants.pingIntervalSecs);
+      ws.pingInterval = hub.engine.liveness.pingInterval;
       final firstText = Completer<String>();
       String? token;
       var welcomed = false;
@@ -534,7 +534,7 @@ void mountSyncRoute(
       void handleIntent(String text) {
         final session = hub.session;
         final viewer = token == null ? null : session.tokens[token];
-        viewer?.touch();
+        viewer?.touch(hub.engine.now);
         Map<String, Object?> decoded;
         try {
           final parsed = jsonDecode(text);

packages/server/lib/src/sync_server.dart

@@ -65,9 +65,13 @@ class SyncServer {
   /// The session log while running with a [logDir].
   SessionLog? get sessionLog => _sessionLog;
 
-  /// [ytDlp] replaces the server's own (tests).
-  SyncServer(this.config, {YtDlp? ytDlp, this.loopbackOnly = false, this.logDir}) {
+  /// [ytDlp] replaces the server's own (tests). [clock] and [liveness]
+  /// go to the engine: a test passes a fake clock to step through the
+  /// silence limits ([Liveness]) without waiting.
+  SyncServer(this.config,
+      {YtDlp? ytDlp, this.loopbackOnly = false, this.logDir, SyncClock? clock, Liveness liveness = const Liveness()}) {
     hub = ServerHub(sessions, config.secret,
+        engine: SyncEngine(clock: clock, liveness: liveness),
         hostKey: config.hostKey,
         jellyfin: config.jellyfin,
         ytDlp: ytDlp ?? YtDlp(serverYtDlpDir(config.ytDlpDir), enabled: config.ytDlp));