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/test/chapters_mpv_e2e_test.dart

@@ -114,7 +114,7 @@ void main() {
         a.seekTo(40);
         await _poll(() {
           final r = a.serverState.peek();
-          return r != null && r.seekBy == a.sync.memberId && (r.position - 40).abs() < 2;
+          return r != null && r.seekBy == a.connection.memberId && (r.position - 40).abs() < 2;
         }, 'server at 0:40');
         await _poll(() => a.skipOffer.peek()?.kind == SkipKind.opening, 'Skip OP offered');
         expect(a.skipOffer.peek()!.target, const Duration(minutes: 2));
@@ -125,9 +125,9 @@ void main() {
         await _poll(() {
           final r = a.serverState.peek();
           return r != null &&
-              r.seekBy == a.sync.memberId &&
-              serverPositionAt(r, a.sync.serverNow()) >= 120 &&
-              serverPositionAt(r, a.sync.serverNow()) < 125;
+              r.seekBy == a.connection.memberId &&
+              serverPositionAt(r, a.connection.serverNow()) >= 120 &&
+              serverPositionAt(r, a.connection.serverNow()) < 125;
         }, 'server at the OP end');
         await _poll(() => b.playback.positionSecs >= 119.5 && b.playback.positionSecs < 126, 'b follows');
         await _poll(() => seeks(b) == seeksBefore + 1, 'b saw the Skip OP seek');