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.

components/seat-autopilot.tsx

@@ -24,6 +24,8 @@ export function SeatAutopilot({ game, act, busy }: SeatAutopilotProps) {
   if (!own || own.bot || !['setup', 'playing'].includes(game.status))
     return null;
 
+  if (game.roomControl?.closed) return <p className="notice">The room is closed. AI play and changes to its control are stopped until an administrator reopens it.</p>;
+
   if (own.autopilot)
     return (
       <section