Keep pregame lobby chat open for an hour after the game ends

The chat used to disappear the moment a session left CREATED status.
Sessions now record a finishedAt timestamp when they're won or lost,
and the lobby (with chat) stays reachable via /game/{session} for an
hour afterward instead of immediately redirecting to the win/lose
feedback page. The lobby template shows a distinct "game finished"
header with a link to that feedback page during this window.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/Game/Controller/GameAdminSessionController.php

@@ -35,6 +35,7 @@ final class GameAdminSessionController extends AbstractController
         }
 
         $session->setStatus(SessionStatus::LOST);
+        $session->setFinishedAt(new \DateTime());
         $em->flush();
 
         $this->addFlash('success', sprintf('Session #%d closed.', $session->getId()));

src/Game/Controller/GameApiController.php

@@ -43,6 +43,7 @@ final class GameApiController extends AbstractController
         if ($session->getStatus() === SessionStatus::PLAYING) {
             if ($session->getTimer() !== null && $now >= $session->getTimer()) {
                 $session->setStatus(SessionStatus::LOST);
+                $session->setFinishedAt(new \DateTime());
                 $this->entityManager->persist($session);
                 $this->entityManager->flush();
                 $isFinished = true;

src/Game/Controller/GameController.php

@@ -149,7 +149,7 @@ final class GameController extends AbstractController
         // Lazily pick up readiness changes from other players since our last request
         $dashboardService->checkAllPlayersReady($session);
 
-        if ($session->getStatus() === SessionStatus::CREATED) {
+        if ($dashboardService->isLobbyChatOpen($session)) {
             return $this->render('game/lobby.html.twig', [
                 'session' => $session,
                 'messages' => $dashboardService->getLobbyMessages($session),