Add administrative room close and reopen controls

Preserve readable private tables, discussion and pending games while closure blocks new play, joins, messages, AI and seat mutations. Add live-authorized atomic closure audits, room-version/revision fences, dedicated controls and exact saved retries. Reopen with the saved pause/join settings and current credentials; restoring a removed but closed room keeps its AI stopped.

Verified types, lint, 5356 offline tests, 52 HTTP tests and build. Seventeen dedicated authenticated HTTP groups and independent privacy/persistence review passed. Desktop/mobile browser QA confirmed one close after a lost response and refresh, persistent readable notices, retained private draft, mobile reopening and saved-seat refresh. All 2,001 baseline rooms, 4,243 seats and related records preserved. Positive production admin acceptance awaits authorized QA access; full admin and rules gates remain open.

app/api/rooms/[code]/control/route.ts

@@ -86,7 +86,7 @@ export async function POST(req: Request) {
                 ownerId: input.ownerId,
                 grantId: input.grantId,
               });
-      if (!result.view.roomControl?.paused && (result.view.botsPending || needsAutomaticRoomRecovery(result.view)))
+      if (!result.view.roomControl?.paused && !result.view.roomControl?.closed && (result.view.botsPending || needsAutomaticRoomRecovery(result.view)))
         waitUntil(resumeRoom(code));
       return Response.json(result, { headers: noStore });
     }