feat(notes): push, long polling and fallback detection for note sync

Phase 4 of the collaboration plan:
- The sync engine listens for DOC_SEQ in the note's realtime room and syncs
  right away. Without WebSocket/SSE it long-polls /docs/{id}/changes (25 s);
  after three failures it falls back to polling every 3 s and retries long
  polling when the browser comes back online.
- With push or long polling the engine only syncs every 7 s while holding
  leases (renewal), otherwise every 30 s as a safety net. Focusing a block
  announces its lease immediately (otherwise it could take up to 30 s).
- Realtime connection: SSE counts as connected only after its first event;
  a stream that stays silent for 5 s (buffering proxy) switches SSE off for
  the tab. App-level PING/PONG detects WebSockets that are accepted but
  forward nothing and switches to SSE after 35 s.
- The editor shows the active channel for shared notes.
- Tests: engine channel tests (push, heartbeat, lease on focus, long
  polling, interval fallback, switching), realtime fallback tests with fake
  WebSocket/EventSource, Go tests for PONG and DOC_SEQ delivery, and
  e2e/channels.e2e.mjs measuring latency behind six simulated proxy setups
  (0.2-0.3 s on all live channels, ~3 s with plain polling).

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

frontend/src/lib/docSync/push.ts

@@ -0,0 +1,25 @@
+// Push notifications for note sync: the server sends DOC_SEQ into the note's room whenever the note, its
+// leases or its presence change. Delivery uses the app-wide realtime connection (WebSocket, else SSE).
+import { createRealtimeConnection, getRealtimeTransport, isRealtimeConnected } from '../api';
+
+export type PushKind = 'ws' | 'sse' | 'none';
+
+export interface PushChannel {
+  /** Calls onPoke for changes of docId and onStatus whenever the channel goes up or down. */
+  subscribe(docId: string, onPoke: () => void, onStatus: (kind: PushKind) => void): () => void;
+}
+
+export const realtimePush: PushChannel = {
+  subscribe(docId, onPoke, onStatus) {
+    const current = (): PushKind => (isRealtimeConnected() ? (getRealtimeTransport() as PushKind) : 'none');
+    const conn = createRealtimeConnection({
+      docId,
+      onMessage: (msg: any) => {
+        if (msg?.event === 'DOC_SEQ' && msg.payload?.docId === docId) onPoke();
+      },
+      onStatusChange: () => onStatus(current()),
+    });
+    onStatus(current());
+    return () => conn.close();
+  },
+};