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>

apps/desktop/lib/src/session/connection.dart

@@ -196,23 +196,30 @@ class Connection {
   final Duration reconnectDelay;
   /// No state broadcast for this long means the connection is lost.
   final Duration silenceLimit;
+  /// The clock [silenceLimit] is measured on (UTC; a test passes a fake
+  /// one). The heartbeat that checks it stays a real 1 s timer.
+  final DateTime Function() now;
 
   Connection(
       {void Function(AppEvent event)? notify,
       SyncClient? client,
       this.hello = defaultHello,
       this.reconnectDelay = const Duration(milliseconds: 1500),
-      this.silenceLimit = const Duration(seconds: 5)})
+      this.silenceLimit = const Duration(seconds: 5),
+      DateTime Function()? now})
       : _notify = notify ?? ((_) {}),
+        now = now ?? _utcNow,
         client = client ?? SyncClient() {
     _subs = [
       this.client.status.listen(_onStatus),
-      this.client.states.listen((_) => _lastStateAt = DateTime.now().toUtc()),
+      this.client.states.listen((_) => _lastStateAt = this.now()),
     ];
   }
 
   late final List<StreamSubscription> _subs;
 
+  static DateTime _utcNow() => DateTime.now().toUtc();
+
   final _state = signal<ConnState>(const ConnClosed());
   /// Every change is notified, a repeat too.
   ReadonlySignal<ConnState> get state => _state;
@@ -368,7 +375,7 @@ class Connection {
       _notify(const ConnectionBack());
     }
     _resumeToken = client.token;
-    _lastStateAt = DateTime.now().toUtc();
+    _lastStateAt = now();
     _set(const ConnOnline());
     _startHeartbeat();
   }
@@ -400,13 +407,13 @@ class Connection {
   /// Every second while connected: a clock sample, the diagnostics, and
   /// the silence check.
   void _beat() {
-    final now = DateTime.now().toUtc();
+    final t = now();
     if (client.token.isNotEmpty) client.sendPing();
     diag
       ..share = AppSettings.instance.shareDiagnostics.peek()
       ..tick();
     final last = _lastStateAt;
-    if (!_closed && last != null && now.difference(last) >= silenceLimit) {
+    if (!_closed && last != null && t.difference(last) >= silenceLimit) {
       _silence.add(null);
       if (!_state.peek().retrying) _dropped();
     }