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.

backend/internal/notify/events.go

@@ -182,8 +182,21 @@ func NotificationGameStarted(userID uuid.UUID, state PlayerState) Intent {
 // NotificationInvitation builds the NotifyInvitation notification carrying the new invitation,
 // so the client adds it to its lobby invitations list without a refetch.
 func NotificationInvitation(userID uuid.UUID, inv InvitationSummary) Intent {
+	return notificationInvitation(userID, NotifyInvitation, inv)
+}
+
+// NotificationInvitationUpdate builds the NotifyInvitationUpdate notification carrying a changed
+// invitation, so the client patches its lobby invitations list without a refetch — upserting a
+// still-pending one (an updated response) and removing one that reached a terminal status.
+func NotificationInvitationUpdate(userID uuid.UUID, inv InvitationSummary) Intent {
+	return notificationInvitation(userID, NotifyInvitationUpdate, inv)
+}
+
+// notificationInvitation builds a KindNotification intent of the given sub-kind carrying the
+// invitation summary; it backs both the new-invitation and invitation-update notifications.
+func notificationInvitation(userID uuid.UUID, sub string, inv InvitationSummary) Intent {
 	b := flatbuffers.NewBuilder(512)
-	k := b.CreateString(NotifyInvitation)
+	k := b.CreateString(sub)
 	invOff := buildInvitation(b, inv)
 	fb.NotificationEventStart(b)
 	fb.NotificationEventAddKind(b, k)

backend/internal/notify/notify.go

@@ -46,7 +46,13 @@ const (
 	// game screen watching that opponent re-derives its "add to friends" state.
 	NotifyFriendDeclined = "friend_declined"
 	NotifyInvitation     = "invitation"
-	NotifyGameStarted    = "game_started"
+	// NotifyInvitationUpdate carries a changed invitation — an updated invitee response, or a
+	// terminal status (started, declined, cancelled, expired) — so the client patches its lobby
+	// invitations list without a refetch. Unlike NotifyInvitation (a brand-new invitation), it is
+	// in-app only: the Telegram connector renders no message for it, so a withdrawal or decline never
+	// becomes an out-of-app push.
+	NotifyInvitationUpdate = "invitation_update"
+	NotifyGameStarted      = "game_started"
 )
 
 // Intent is one live event destined for a single user. Payload is the

backend/internal/notify/notify_test.go

@@ -181,6 +181,23 @@ func TestNotificationInvitationCarriesInvitation(t *testing.T) {
 	}
 }
 
+func TestNotificationInvitationUpdateCarriesTerminalInvitation(t *testing.T) {
+	uid := uuid.New()
+	inv := notify.InvitationSummary{ID: "inv-9", Variant: "scrabble_en", Status: "declined"}
+	in := notify.NotificationInvitationUpdate(uid, inv)
+	if in.Kind != notify.KindNotification {
+		t.Fatalf("kind = %q", in.Kind)
+	}
+	ev := fb.GetRootAsNotificationEvent(in.Payload, 0)
+	if string(ev.Kind()) != notify.NotifyInvitationUpdate {
+		t.Fatalf("sub-kind = %q, want %q", ev.Kind(), notify.NotifyInvitationUpdate)
+	}
+	got := ev.Invitation(nil)
+	if got == nil || string(got.Id()) != "inv-9" || string(got.Status()) != "declined" {
+		t.Fatalf("invitation wrong: %+v", got)
+	}
+}
+
 func TestNotificationAccountCarriesAccount(t *testing.T) {
 	uid := uuid.New()
 	in := notify.NotificationAccount(uid, notify.NotifyFriendRequest, notify.AccountRef{AccountID: "a-1", DisplayName: "Ann"})