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>

backend/internal/lobby/deps.go

@@ -9,14 +9,21 @@ import (
 
 // EntitlementProvider is the read-only view the lobby needs over the
 // user-domain entitlement snapshot. The canonical implementation is
-// `*user.Service` exposing `GetEntitlement(ctx, userID)`; tests substitute
-// a fake.
+// `*user.Service` exposing `GetEntitlementSnapshot(ctx, userID)`; tests
+// substitute a fake.
 //
-// `MaxRegisteredRaceNames` is the only field consumed by when
-// the caller attempts to register a `pending_registration` row the lobby
-// counts already-`registered` rows for that user against this limit.
+// `GetMaxRegisteredRaceNames` is consumed at race-name registration time
+// — when the caller attempts to register a `pending_registration` row the
+// lobby counts already-`registered` rows for that user against this limit.
+//
+// `IsPaid` is consumed by the user-facing private-game creation gate at
+// the HTTP handler level (`POST /api/v1/user/lobby/games`): free-tier
+// callers are rejected with `403 forbidden` before the lobby Service is
+// invoked. Admin-driven public-game creation
+// (`POST /api/v1/admin/games`) bypasses the gate.
 type EntitlementProvider interface {
 	GetMaxRegisteredRaceNames(ctx context.Context, userID uuid.UUID) (int32, error)
+	IsPaid(ctx context.Context, userID uuid.UUID) (bool, error)
 }
 
 // RuntimeGateway is the outbound surface the lobby uses to ask the runtime