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/app.svelte.ts

@@ -27,7 +27,7 @@ import { connection, reportOffline, reportOnline, resetConnection } from './conn
 import { isConnectionCode } from './retry';
 import { clearGameCache, getCachedGame, setCachedGame } from './gamecache';
 import { advanceCached } from './gamedelta';
-import { clearLobby, patchLobbyGame } from './lobbycache';
+import { clearLobby, patchLobbyGame, patchLobbyInvitation } from './lobbycache';
 import type { BoardLabelMode } from './boardlabels';
 
 export interface Toast {
@@ -191,9 +191,16 @@ function openStream(): void {
           if (c) setCachedGame(e.gameId, c.view, c.moves);
         }
       } else if (e.kind === 'opponent_joined') {
-        // The opponent took an open game's empty seat: mirror the new status into the lobby snapshot
-        // from any screen. A mounted game board adopts the change in place itself (game/Game.svelte).
-        if (e.state) patchLobbyGame(e.state.game);
+        // The opponent took an open game's empty seat: mirror the new status into the lobby snapshot,
+        // and warm a not-currently-viewed game's own cache, so opening it from any screen is flash-free.
+        // The mounted game board owns its cache (game/Game.svelte), so skip the game in view.
+        if (e.state) {
+          patchLobbyGame(e.state.game);
+          if (!viewingGame(e.gameId)) {
+            const c = advanceCached(getCachedGame(e.gameId), e);
+            if (c) setCachedGame(e.gameId, c.view, c.moves);
+          }
+        }
       } else if (e.kind === 'match_found') {
         // Seed both caches from the event's initial state so the game renders instantly on arrival
         // and the new game is already in the lobby on a later return, then navigate.
@@ -209,6 +216,12 @@ function openStream(): void {
           setCachedGame(e.state.game.id, e.state, []);
           patchLobbyGame(e.state.game);
         }
+        // An invitation created / updated / withdrawn elsewhere: keep the lobby's invitations list
+        // fresh from any screen — a new pending one is added, a consumed (started), declined,
+        // cancelled or expired one is removed (see patchLobbyInvitation).
+        if ((e.sub === 'invitation' || e.sub === 'invitation_update') && e.invitation) {
+          patchLobbyInvitation(e.invitation);
+        }
         void refreshNotifications();
       }
     },