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>

docs/ARCHITECTURE.md

@@ -142,7 +142,9 @@ because they cross domain boundaries:
 - **Public lobby games are admin-created** through
   `POST /api/v1/admin/games`. The user-facing
   `POST /api/v1/user/lobby/games` always emits `private` games owned by
-  `X-User-ID`. Public games carry `owner_user_id IS NULL`; the partial
+  `X-User-ID`, and is gated by `EntitlementProvider.IsPaid` — free-tier
+  callers receive `403 forbidden` before the lobby service is invoked.
+  Public games carry `owner_user_id IS NULL`; the partial
   index on `(owner_user_id) WHERE visibility = 'private'` keeps the
   private-owner lookup efficient.
 - **Authenticated lobby commands** flow through the gateway envelope