fix(dp): address TPVR review findings (DP2 redo, DP4 dedup, DP15 gap)

- DP2: the earlier seed fix was ineffective (allInvitesAtom populates post-mount,
  so first render is still empty). Rewrite to track invite room ids and stay
  'unarmed' until the initial sync settles (+3s grace), notifying only for ids that
  first appear after arming — robust to the async population race.
- DP4: batch the mutually-exclusive tag writes via Promise.all so a failure surfaces
  a single toast instead of one per operation.
- DP15: route the two remaining StateEvent writes (RoomSoundboardPack / RoomImagePack,
  which used an 'as unknown as keyof StateEvents' idiom the sweep missed) through the
  typed sendStateEvent helper.

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

src/app/components/soundboard-pack-view/RoomSoundboardPack.tsx

@@ -5,6 +5,7 @@ import { useMatrixClient } from '../../hooks/useMatrixClient';
 import { SoundboardPackEditor } from './SoundboardPackEditor';
 import { SoundboardContent, SoundboardPack } from '../../plugins/soundboard';
 import { StateEvent } from '../../../types/matrix/room';
+import { sendStateEvent } from '../../utils/room';
 import { useRoomSoundboardPack } from '../../hooks/useSoundboardPacks';
 import { PackAddress } from '../../plugins/custom-emoji/PackAddress';
 import { randomStr } from '../../utils/common';
@@ -35,12 +36,7 @@ export function RoomSoundboardPack({ room, stateKey }: RoomSoundboardPackProps)
 
   const handleUpdate = useCallback(
     async (content: SoundboardContent) => {
-      await mx.sendStateEvent(
-        room.roomId,
-        StateEvent.LotusSoundboardRoom as unknown as keyof import('matrix-js-sdk').StateEvents,
-        content as never,
-        stateKey,
-      );
+      await sendStateEvent(mx, room.roomId, StateEvent.LotusSoundboardRoom, content, stateKey);
     },
     [mx, room.roomId, stateKey],
   );