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>

integration/engine_command_proxy_test.go

@@ -29,6 +29,7 @@ func TestEngineCommandProxy(t *testing.T) {
 	}
 
 	owner := testenv.RegisterSession(t, plat, "owner+cmd@example.com")
+	testenv.PromoteToPaid(t, ctx, admin, plat, owner)
 	ownerID, err := owner.LookupUserID(ctx, plat)
 	if err != nil {
 		t.Fatalf("resolve owner: %v", err)