Restructure step 0: Connection extracted from the coordinator

Connection owns the socket lifecycle, connect/dial with epochs,
reconnect, the clock offset, diagnostics upload and a sealed ConnState
signal; the hello is built by an injectable builder, the resume token
stays private, and the reconnect delay and silence limit are parameters.
The coordinator maps ConnState to the same health texts and keeps the
reconnect restore and drop handling (step 1 replaces them).

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

apps/desktop/lib/src/state/session_state.dart

@@ -18,6 +18,7 @@ import '../sfx/sound_bank.dart';
 import '../sfx/synth_sfx.dart';
 import '../session/health.dart';
 import '../session/notifier.dart';
+import '../session/connection.dart' show Connection;
 import '../session/session_coordinator.dart';
 import '../widgets/avatar_pipeline.dart';
 import 'connect_prefs.dart';
@@ -173,7 +174,10 @@ class SessionState {
   final Ports ports = desktopPorts();
   /// Every toast, sound and activity-log line goes through it.
   late final Notifier notifier = Notifier(sfx: sfx, attention: ports.shell.requestAttention);
-  late final SessionCoordinator coordinator = SessionCoordinator(notifier: notifier, ytDlp: ports.links);
+  /// The link to the server; lost/back go to the notifier.
+  late final Connection connection = Connection(notify: notifier.notify);
+  late final SessionCoordinator coordinator =
+      SessionCoordinator(notifier: notifier, connection: connection, ytDlp: ports.links);
   final lastForm = ConnectForm();
   JellyfinAccounts get jellyfin => JellyfinAccounts.instance;
   /// Set when the hosted server died mid-session; Home shows it on the
@@ -348,7 +352,7 @@ class SessionState {
     });
     try {
       await landed.future.timeout(const Duration(seconds: 20));
-      coordinator.sync.sendSeek(carry.position);
+      coordinator.connection.sendSeek(carry.position);
     } on TimeoutException {
       debugPrint('resume: the media did not come up; not seeking');
     } finally {