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/server/handlers_user_lobby_games.go

@@ -86,6 +86,15 @@ func (h *UserLobbyGamesHandlers) Create() gin.HandlerFunc {
 			return
 		}
 		ctx := c.Request.Context()
+		paid, err := h.svc.IsPaid(ctx, userID)
+		if err != nil {
+			respondLobbyError(c, h.logger, "user lobby games create", ctx, err)
+			return
+		}
+		if !paid {
+			httperr.Abort(c, http.StatusForbidden, httperr.CodeForbidden, "creating private games requires a paid subscription")
+			return
+		}
 		owner := userID
 		game, err := h.svc.CreateGame(ctx, lobby.CreateGameInput{
 			OwnerUserID: &owner,