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)