fix(state): correct invite re-notify, status clear sync, soundboard resync (DP2/DP3/DP5)

- Invites: seed the notify baseline with the invite count at mount instead
  of 0, so a warm reload (allInvitesAtom populates synchronously from cache
  while SYNCING) no longer re-fires the toast+sound for pre-existing invites.
  Only a genuine increase notifies.
- Status: the cross-device sync effect gated on a truthy presence.status, so
  a remote CLEAR never reset the input or localStorage[STATUS_MSG_KEY] and
  usePresenceUpdater.readStatus() re-sent the stale status. Now mirror an
  empty status as a clear (skipping offline/invisible, which carries an empty
  status_msg by design).
- Soundboard: useState initializers ran once and never recomputed when the
  room/rooms arg changed. Add a resync effect keyed on the arg while keeping
  the live state-event update path.

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

src/app/features/settings/account/Profile.tsx

@@ -52,7 +52,7 @@ import { ModalWide } from '../../../styles/Modal.css';
 import { createUploadAtom, UploadSuccess } from '../../../state/upload';
 import { CompactUploadCardRenderer } from '../../../components/upload-card';
 import { useCapabilities } from '../../../hooks/useCapabilities';
-import { useUserPresence } from '../../../hooks/useUserPresence';
+import { Presence, useUserPresence } from '../../../hooks/useUserPresence';
 import { ProfileDecoration } from './ProfileDecoration';
 import { EmojiBoard } from '../../../components/emoji-board';
 
@@ -365,13 +365,26 @@ function ProfileStatus() {
 
   // Sync input when another device changes the status.
   // Skipped while the user has unsaved local edits to avoid clobbering
-  // mid-flight input (e.g. an emoji being inserted).
+  // mid-flight input (e.g. an emoji being inserted), and while presence data has
+  // not loaded yet (presence === undefined is "no info", NOT a clear).
   useEffect(() => {
-    if (!statusDirtyRef.current && presence?.status) {
-      setStatusMsg(presence.status);
-      localStorage.setItem(STATUS_MSG_KEY(userId), presence.status);
+    if (statusDirtyRef.current || !presence) return;
+    // An offline/invisible presence carries an empty status_msg by design (see
+    // usePresenceUpdater.setOffline), so ignore it — reading it as a clear would
+    // wipe the saved status on every invisible toggle.
+    if (presence.presence === Presence.Offline) return;
+    const remoteStatus = presence.status ?? '';
+    if (remoteStatus) {
+      setStatusMsg(remoteStatus);
+      localStorage.setItem(STATUS_MSG_KEY(userId), remoteStatus);
+    } else {
+      // Another device CLEARED the status. Mirror it locally AND drop the stored
+      // value, otherwise usePresenceUpdater.readStatus() re-sends the stale
+      // message on the next presence heartbeat.
+      setStatusMsg('');
+      localStorage.removeItem(STATUS_MSG_KEY(userId));
     }
-  }, [presence?.status, userId]);
+  }, [presence, userId]);
 
   const [saveState, saveStatus] = useAsyncCallback(
     useCallback(