feat(lobby): keep lobby/game caches fresh from any screen + invitation delta channel

Builds on the cross-screen cache work: the global stream handler now keeps both
caches current no matter which screen is mounted, and invitations become a live
delta channel so the lobby's invitations list is fresh from any screen too.

Client (boundary already started):
- advanceCached now also folds opponent_joined into a not-currently-viewed game's
  cache via a new pure reducer applyOpponentJoined (extracted and reused by the
  mounted game board), so opening an open game that filled while you were elsewhere
  is flash-free.
- patchLobbyInvitation upserts a still-pending invitation and removes a terminal
  one (started/declined/cancelled/expired); the global notify handler calls it on
  the invitation / invitation_update sub-kinds.

Invitations delta channel (no wire/gateway/connector change — the notification
already carries the full invitation with id/status/game_id end to end):
- notify: a new in-app-only NotifyInvitationUpdate sub + NotificationInvitationUpdate
  constructor (shares encoding with NotificationInvitation). The Telegram connector
  renders no message for it, so a decline/cancel never becomes an out-of-app push.
- lobby: emit the changed invitation to every participant on respond (accept/decline),
  on the final accept's game start, and on cancel — so each participant's lobby patches
  its list in place. The authoritative list holds only pending invitations, so the
  client's pending-vs-terminal rule matches it exactly.

Tests: applyOpponentJoined + patchLobbyInvitation unit tests (TDD), the
NotificationInvitationUpdate encoding unit test, and integration assertions that
decline/cancel/accept publish invitation_update to every participant. Full local
suite green (backend unit+integration, UI check/unit/build/bundle/e2e). Docs:
ARCHITECTURE §10 (notify catalog + in-app-only note) and UI_DESIGN updated.

ui/src/lib/gamedelta.test.ts

@@ -1,5 +1,5 @@
 import { describe, expect, it } from 'vitest';
-import { advanceCached, applyGameOver, applyMoveDelta, seedInitialState, type MoveDelta } from './gamedelta';
+import { advanceCached, applyGameOver, applyMoveDelta, applyOpponentJoined, seedInitialState, type MoveDelta } from './gamedelta';
 import type { CachedGame } from './gamecache';
 import type { GameView, MoveRecord, PushEvent, StateView } from './model';
 
@@ -141,3 +141,30 @@ describe('advanceCached', () => {
     expect(advanceCached(cache(3, 0), yourTurn)).toBeUndefined();
   });
 });
+
+describe('applyOpponentJoined', () => {
+  // joinedState is the refreshed StateView an opponent_joined event carries: the open game is now
+  // active and both seats are filled.
+  function joinedState(): StateView {
+    const game: GameView = { ...gameView(0), status: 'active', players: 2, seats: [
+      { seat: 0, accountId: 'me', displayName: 'Me', score: 0, hintsUsed: 0, isWinner: false },
+      { seat: 1, accountId: 'opp', displayName: 'Opp', score: 0, hintsUsed: 0, isWinner: false },
+    ] };
+    return { game, seat: 0, rack: ['x'], bagLen: 90, hintsRemaining: 0 };
+  }
+
+  it("adopts the joined seats and status while preserving the cached rack and moves", () => {
+    // The cached open game is still "searching": empty seats, status open, the starter's own rack.
+    const cached: CachedGame = { view: { game: { ...gameView(2), status: 'open', seats: [] }, seat: 0, rack: ['a', 'b'], bagLen: 50, hintsRemaining: 1 }, moves: [move(0)] };
+    const res = applyOpponentJoined(cached, joinedState());
+    expect(res?.view.game.status).toBe('active');
+    expect(res?.view.game.seats).toHaveLength(2);
+    expect(res?.view.rack).toEqual(['a', 'b']); // the starter's rack is untouched by the join
+    expect(res?.view.game.moveCount).toBe(2); // the cached count/board is preserved
+    expect(res?.moves).toHaveLength(1);
+  });
+
+  it('returns undefined when nothing is cached for the game', () => {
+    expect(applyOpponentJoined(undefined, joinedState())).toBeUndefined();
+  });
+});