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>

internal/ws/hub.go

@@ -631,7 +631,10 @@ func (c *Client) readPump() {
 			}
 
 			// Room subscription without requiring docID
-			if incoming.Event == "JOIN_ROOM" {
+			if incoming.Event == "PING" {
+				// App-level heartbeat: lets clients detect proxies that accept the upgrade but forward nothing
+				c.SendEvent("PONG", nil)
+			} else if incoming.Event == "JOIN_ROOM" {
 				room := incoming.Room
 				if room == "" {
 					room = docID