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/lobby_e2e_test.go

@@ -103,6 +103,10 @@ func (s stubEntitlement) GetMaxRegisteredRaceNames(_ context.Context, _ uuid.UUI
 	return s.max, nil
 }
 
+func (s stubEntitlement) IsPaid(_ context.Context, _ uuid.UUID) (bool, error) {
+	return true, nil
+}
+
 func newServiceForTest(t *testing.T, db *sql.DB, now func() time.Time, max int32) *lobby.Service {
 	t.Helper()
 	store := lobby.NewStore(db)