feat(lobby): F8-04b hierarchical sidebar + paid-tier gate for create-game

Reshape the lobby UI from a single Overview into a two-level sidebar
(games · profile · DEV synthetic-reports) with four games sub-panels
(active-past · recruitment · invitations · private-games). Move the
`create new game` button into the private-games panel, merge the
applications section into recruitment cards as status chips, and add
DEV-only synthetic-report loader as a top-level screen.

Add a paid-tier gate at backend `lobby.game.create`: free callers get
`403 forbidden` before the lobby service is invoked. The UI hides the
private-games sub-panel + create button on free tier (DEV affordances
flag overrides). Update every integration test that creates a game to
use a new `testenv.PromoteToPaid` helper; add a new
`TestLobbyFlow_FreeUserCreateGameForbidden`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

ui/frontend/src/app.d.ts

@@ -7,7 +7,17 @@ declare global {
 		// (and active game) live in `page.state` so browser Back/Forward
 		// move between screens while the address bar stays at /game/.
 		interface PageState {
-			screen?: "login" | "lobby" | "lobby-create" | "profile" | "game";
+			screen?:
+				| "login"
+				| "lobby"
+				| "lobby-create"
+				| "profile"
+				| "game"
+				| "games-active-past"
+				| "games-recruitment"
+				| "games-invitations"
+				| "games-private-games"
+				| "synthetic-reports";
 			gameId?: string | null;
 		}
 	}