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();
       }
     },

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();
+  });
+});

ui/src/lib/gamedelta.ts

@@ -82,5 +82,19 @@ export function advanceCached(cached: CachedGame | undefined, e: PushEvent): Cac
     return applyMoveDelta(cached, { move: e.move, game: e.game, bagLen: e.bagLen }).cache;
   }
   if (e.kind === 'game_over') return applyGameOver(cached, e.game).cache;
+  if (e.kind === 'opponent_joined' && e.state) return applyOpponentJoined(cached, e.state);
   return undefined;
 }
+
+/**
+ * applyOpponentJoined adopts an opponent_joined event into a cached open game: it overlays the
+ * refreshed seats, status and player count from the event's StateView onto the cached game, leaving
+ * the board, the starter's rack and everything else intact (the join changes who is seated, not the
+ * position). It returns undefined when the game is not cached (the next open cold-loads it). It backs
+ * both the mounted game board's in-place update and the global handler's off-screen cache warming.
+ */
+export function applyOpponentJoined(cached: CachedGame | undefined, state: StateView): CachedGame | undefined {
+  if (!cached) return undefined;
+  const game: GameView = { ...cached.view.game, seats: state.game.seats, status: state.game.status, players: state.game.players };
+  return { view: { ...cached.view, game }, moves: cached.moves };
+}

ui/src/lib/lobbycache.test.ts

@@ -1,6 +1,23 @@
 import { beforeEach, describe, expect, it } from 'vitest';
-import { clearLobby, getLobby, patchLobbyGame, setLobby } from './lobbycache';
-import type { AccountRef, GameView } from './model';
+import { clearLobby, getLobby, patchLobbyGame, patchLobbyInvitation, setLobby } from './lobbycache';
+import type { AccountRef, GameView, Invitation } from './model';
+
+function invitation(id: string, status: string): Invitation {
+  return {
+    id,
+    inviter: { accountId: 'inv', displayName: 'Inv' },
+    invitees: [],
+    variant: 'scrabble_en',
+    turnTimeoutSecs: 300,
+    hintsAllowed: true,
+    hintsPerPlayer: 0,
+    multipleWordsPerTurn: true,
+    dropoutTiles: 'remove',
+    status,
+    gameId: '',
+    expiresAtUnix: 0,
+  };
+}
 
 function gameView(id: string, status: GameView['status'] = 'active', toMove = 0): GameView {
   return {
@@ -59,3 +76,46 @@ describe('patchLobbyGame', () => {
     expect(games[0].toMove).toBe(0); // the original array/object is left intact
   });
 });
+
+describe('patchLobbyInvitation', () => {
+  it('adds a new pending invitation to the cached lobby', () => {
+    setLobby({ games: [], invitations: [], incoming: [] });
+    patchLobbyInvitation(invitation('i1', 'pending'));
+    expect(getLobby()?.invitations.map((x) => x.id)).toEqual(['i1']);
+  });
+
+  it('replaces a pending invitation already in the list (e.g. an updated response)', () => {
+    setLobby({ games: [], invitations: [invitation('i1', 'pending'), invitation('i2', 'pending')], incoming: [] });
+    const updated = { ...invitation('i1', 'pending'), turnTimeoutSecs: 999 };
+    patchLobbyInvitation(updated);
+    expect(getLobby()?.invitations.map((x) => x.id)).toEqual(['i1', 'i2']);
+    expect(getLobby()?.invitations.find((x) => x.id === 'i1')?.turnTimeoutSecs).toBe(999);
+  });
+
+  it('removes an invitation that reached a terminal status', () => {
+    for (const terminal of ['declined', 'cancelled', 'started', 'expired']) {
+      setLobby({ games: [], invitations: [invitation('i1', 'pending'), invitation('i2', 'pending')], incoming: [] });
+      patchLobbyInvitation(invitation('i1', terminal));
+      expect(getLobby()?.invitations.map((x) => x.id)).toEqual(['i2']);
+    }
+  });
+
+  it('is a no-op for a terminal invitation that is not in the list', () => {
+    setLobby({ games: [], invitations: [invitation('i2', 'pending')], incoming: [] });
+    patchLobbyInvitation(invitation('i1', 'declined'));
+    expect(getLobby()?.invitations.map((x) => x.id)).toEqual(['i2']);
+  });
+
+  it('is a no-op when there is no cached lobby yet', () => {
+    patchLobbyInvitation(invitation('i1', 'pending'));
+    expect(getLobby()).toBeNull();
+  });
+
+  it('preserves games and incoming when patching an invitation', () => {
+    const incoming: AccountRef[] = [{ accountId: 'u9', displayName: 'Nine' }];
+    setLobby({ games: [gameView('g1')], invitations: [], incoming });
+    patchLobbyInvitation(invitation('i1', 'pending'));
+    expect(getLobby()?.games.map((g) => g.id)).toEqual(['g1']);
+    expect(getLobby()?.incoming).toEqual(incoming);
+  });
+});

ui/src/lib/lobbycache.ts

@@ -42,6 +42,31 @@ export function patchLobbyGame(g: GameView): void {
   snapshot = { ...snapshot, games };
 }
 
+/**
+ * patchLobbyInvitation applies a live invitation change to the cached lobby's invitations list, so a
+ * change seen while the lobby is unmounted is reflected on its next render instead of a stale card
+ * lingering until the background refresh. A still-pending invitation is upserted (a new one
+ * prepended newest-first, an updated one replaced in place); an invitation that reached any terminal
+ * status (started, declined, cancelled, expired) is removed — the authoritative list holds only
+ * pending invitations. It is a no-op when there is no snapshot yet, or a terminal invitation is not
+ * in the list. The lobby re-renders from the snapshot, so the in-place upsert needs no re-sort.
+ */
+export function patchLobbyInvitation(inv: Invitation): void {
+  if (!snapshot) return;
+  const i = snapshot.invitations.findIndex((x) => x.id === inv.id);
+  let invitations: Invitation[];
+  if (inv.status !== 'pending') {
+    if (i === -1) return; // a terminal invitation already absent — nothing to remove
+    invitations = snapshot.invitations.filter((x) => x.id !== inv.id);
+  } else if (i === -1) {
+    invitations = [inv, ...snapshot.invitations];
+  } else {
+    invitations = snapshot.invitations.slice();
+    invitations[i] = inv;
+  }
+  snapshot = { ...snapshot, invitations };
+}
+
 /** clearLobby drops the cached lobby (called on logout). */
 export function clearLobby(): void {
   snapshot = null;