Fix host reconnection losing player state and first-answer bonus

- Persist firstCorrectPlayerId to backend during state sync
- Restore full players array (not just host) on host reconnect
- Add default values to WELCOME payload for new/unmatched players
- Add migration for first_correct_player_id column in game_sessions

hooks/useGame.ts

@@ -71,7 +71,8 @@ export const useGame = () => {
   const gameConfigRef = useRef<GameConfig>(DEFAULT_GAME_CONFIG);
   const gamePinRef = useRef<string | null>(null);
   const hostSecretRef = useRef<string | null>(null);
-  const gameStateRef = useRef<GameState>('LANDING');
+  const gameStateRef = useRef<GameState>("LANDING");
+  const firstCorrectPlayerIdRef = useRef<string | null>(null);
 
   useEffect(() => { timeLeftRef.current = timeLeft; }, [timeLeft]);
   useEffect(() => { playersRef.current = players; }, [players]);
@@ -81,6 +82,7 @@ export const useGame = () => {
   useEffect(() => { gamePinRef.current = gamePin; }, [gamePin]);
   useEffect(() => { hostSecretRef.current = hostSecret; }, [hostSecret]);
   useEffect(() => { gameStateRef.current = gameState; }, [gameState]);
+  useEffect(() => { firstCorrectPlayerIdRef.current = firstCorrectPlayerId; }, [firstCorrectPlayerId]);
 
   const generateGamePin = () => Math.floor(Math.random() * 900000) + 100000 + "";
 
@@ -98,6 +100,7 @@ export const useGame = () => {
         body: JSON.stringify({
           gameState: gameStateRef.current,
           currentQuestionIndex: currentQuestionIndexRef.current,
+          firstCorrectPlayerId: firstCorrectPlayerIdRef.current,
           players: playersRef.current,
         }),
       });
@@ -296,6 +299,7 @@ export const useGame = () => {
     setQuiz(hostData.quiz);
     setGameConfig(hostData.gameConfig);
     setCurrentQuestionIndex(hostData.currentQuestionIndex || 0);
+    setFirstCorrectPlayerId(hostData.firstCorrectPlayerId || null);
     
     const hostPlayer = (hostData.players || []).find((p: Player) => p.id === 'host');
     if (hostPlayer) {
@@ -303,7 +307,7 @@ export const useGame = () => {
       setCurrentPlayerName('Host');
       setCurrentPlayerScore(hostPlayer.score);
       setCurrentStreak(hostPlayer.streak);
-      setPlayers([hostPlayer]);
+      setPlayers(hostData.players || []);
       
       if (hostPlayer.lastAnswerCorrect !== null) {
         setHasAnswered(true);