feat(extension): host control mode guest UX in content script (step 4)

Guest-side handling when a room is in host-only mode:

- Intent classifier (EC-9): tells a deliberate guest pause/seek from an
  involuntary one (buffering/seeking/tab-refocus/no recent gesture) via
  readyState, video.seeking, a 'waiting' buffering-grace window, the existing
  visibility grace, and own-tracked keydown/pointerdown gestures.
- HOST_BLOCKED handler: live streams are left alone (EC-15); involuntary events
  snap back silently; deliberate events show a Teleparty-style choice dialog
  (Stay in sync / Watch on my own), defaulting to stay after 8s (EC-18).
- Snap-back reuses tryMediaAction + suppress, with a cooldown to avoid
  pause/play fight loops (EC-4).
- Desync ("watch on my own") mode: persistent resync badge, ignores host
  commands while solo (still ACKs so force-sync doesn't stall), and auto-clears
  on episode change (EC-12). Resync pulls the host's extrapolated position.
- background: GET_CONTROL_MODE (init fetch) + REQUEST_HOST_SYNC (resync target).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

extension/background.js

@@ -1683,6 +1683,12 @@ async function handleAsyncMessage(message, sender, sendResponse) {
         }
         emit(EVENTS.SET_CONTROL_MODE, { controlMode: mode });
         sendResponse({ status: 'ok' });
+    } else if (message.type === 'GET_CONTROL_MODE') {
+        // content.js asks for current mode/role (e.g. injected after ROOM_DATA).
+        sendResponse({ controlMode, hostPeerId, amHost: amHost() });
+    } else if (message.type === 'REQUEST_HOST_SYNC') {
+        // content.js resync: hand back the host's extrapolated current position.
+        sendResponse({ target: getHostSyncTarget() });
     } else if (message.type === 'LEAVE_ROOM') {
         connectIntent = false;
         reconnectFailed = false;