Add game start functionality with automatic player chip generation

Implemented host-controlled game start mechanism that generates unique player chips from user names. Added `started_at` timestamp to games and new `game_chips` table to store player identifiers. Chips are created using first name initial plus first two surname letters (e.g., SNE for Sascha Nesterovic) with automatic conflict resolution. Updated frontend to display start button for hosts, show game status, and populate chip selection modal

frontend/src/App.jsx

@@ -50,6 +50,7 @@ export default function App() {
   // Game meta
   const [gameMeta, setGameMeta] = useState(null); // {code, host_user_id, winner_email, winner_user_id}
   const [members, setMembers] = useState([]);
+  const [gameChips, setGameChips] = useState([]);
 
   // Winner selection (host only)
   const [winnerUserId, setWinnerUserId] = useState("");
@@ -138,6 +139,9 @@ export default function App() {
     setGameMeta(meta);
     setWinnerUserId(meta?.winner_user_id || "");
 
+    const chips = meta?.started ? await api(`/games/${gameId}/chips`) : [];
+    setGameChips(chips || []);
+
     const mem = await api(`/games/${gameId}/members`);
     setMembers(mem);
 
@@ -327,6 +331,7 @@ export default function App() {
     setSheet(null);
     setGameMeta(null);
     setMembers([]);
+    setGameChips([]);
     setWinnerUserId("");
 
     // reset winner celebration on logout
@@ -431,6 +436,7 @@ export default function App() {
     setSheet(null);
     setGameMeta(null);
     setMembers([]);
+    setGameChips([]);
     setWinnerUserId("");
     setPulseId(null);
 
@@ -469,6 +475,12 @@ export default function App() {
     setGameId(res.id);
   };
 
+  const startGame = async () => {
+    if (!gameId || !gameMeta?.host_user_id || me?.id !== gameMeta.host_user_id) return;
+    await api(`/games/${gameId}/start`, { method: "POST" });
+    await loadGameMeta();
+  };
+
   // ===== Winner =====
   const saveWinner = async () => {
     if (!gameId) return;
@@ -501,6 +513,10 @@ export default function App() {
     const next = cycleTag(entry.note_tag);
 
     if (next === "s") {
+      if (!gameMeta?.started || gameChips.length === 0) {
+        showSnack("Das Spiel muss zuerst gestartet werden.");
+        return;
+      }
       setChipEntry(entry);
       setChipOpen(true);
       return;
@@ -642,6 +658,10 @@ export default function App() {
           members={members}
           me={me}
           hostUserId={gameMeta?.host_user_id || ""}
+          isHost={isHost}
+          started={!!gameMeta?.started}
+          chipCount={gameChips.length}
+          onStartGame={startGame}
         />
 
         {/* Sieger Badge: zwischen Spiel und Verdächtigte Person */}
@@ -717,6 +737,7 @@ export default function App() {
         chipOpen={chipOpen}
         closeChipModalToDash={closeChipModalToDash}
         chooseChip={chooseChip}
+        chips={gameChips}
       />
 
       <StatsModal