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/cmd/backend/main.go

@@ -485,6 +485,17 @@ func (a *userEntitlementAdapter) GetMaxRegisteredRaceNames(ctx context.Context,
 	return snap.MaxRegisteredRaceNames, nil
 }
 
+func (a *userEntitlementAdapter) IsPaid(ctx context.Context, userID uuid.UUID) (bool, error) {
+	if a == nil || a.svc == nil {
+		return false, nil
+	}
+	snap, err := a.svc.GetEntitlementSnapshot(ctx, userID)
+	if err != nil {
+		return false, err
+	}
+	return snap.IsPaid, nil
+}
+
 // runtimeGatewayAdapter implements `lobby.RuntimeGateway` by
 // delegating to `*runtime.Service`. The svc pointer is patched after
 // the services are constructed — runtime depends on lobby