Enhance member display in GamePickerCard and remove redundancy

Added functionality to display members in GamePickerCard, replacing the previously redundant implementation in NewGameModal. This change centralizes member display logic, reducing code duplication and improving maintainability.

frontend/src/App.jsx

@@ -514,6 +514,7 @@ export default function App() {
           gameId={gameId}
           setGameId={setGameId}
           onOpenHelp={() => setHelpOpen(true)}
+          members={members}
         />
 
         {/* Sieger Badge: zwischen Spiel und Verdächtigte Person */}

frontend/src/components/GamePickerCard.jsx

@@ -2,7 +2,7 @@ import React from "react";
 import { styles } from "../styles/styles";
 import { stylesTokens } from "../styles/theme";
 
-export default function GamePickerCard({ games, gameId, setGameId, onOpenHelp }) {
+export default function GamePickerCard({ games, gameId, setGameId, onOpenHelp, members = [] }) {
   return (
     <div style={{ marginTop: 14 }}>
       <div style={styles.card}>
@@ -36,6 +36,37 @@ export default function GamePickerCard({ games, gameId, setGameId, onOpenHelp })
             </div>
           );
         })()}
+
+        {members?.length > 0 && (
+          <div style={{ marginTop: 8 }}>
+            <div style={{ fontSize: 12, opacity: 0.8, color: stylesTokens.textDim }}>
+              Spieler ({members.length})
+            </div>
+
+            <div style={{ marginTop: 6, display: "flex", flexWrap: "wrap", gap: 8 }}>
+              {members.map((m) => {
+                const name = ((m.display_name || "").trim() || (m.email || "").trim() || "—");
+                return (
+                  <div
+                    key={m.id}
+                    style={{
+                      padding: "6px 10px",
+                      borderRadius: 999,
+                      border: "1px solid rgba(233,216,166,0.18)",
+                      background: "rgba(10,10,12,0.35)",
+                      color: stylesTokens.textMain,
+                      fontSize: 13,
+                      fontWeight: 900,
+                    }}
+                  >
+                    {name}
+                  </div>
+                );
+              })}
+            </div>
+          </div>
+        )}
+
       </div>
     </div>
   );

frontend/src/components/NewGameModal.jsx

@@ -12,7 +12,6 @@ export default function NewGameModal({
   currentCode = "",
   gameFinished = false,
   hasGame = false,
-  currentMembers = [],
 }) {
   // modes: running | choice | create | join
   const [mode, setMode] = useState("choice");
@@ -169,46 +168,6 @@ export default function NewGameModal({
             </>
           )}
 
-          {currentMembers?.length > 0 && (
-            <div
-              style={{
-                marginTop: 10,
-                padding: 10,
-                borderRadius: 14,
-                border: `1px solid ${stylesTokens.panelBorder}`,
-                background: stylesTokens.panelBg,
-                display: "grid",
-                gap: 8,
-              }}
-            >
-              <div style={{ fontSize: 12, opacity: 0.8, color: stylesTokens.textDim }}>
-                Aktuelle Spieler ({currentMembers.length})
-              </div>
-
-              <div style={{ display: "flex", flexWrap: "wrap", gap: 8 }}>
-                {currentMembers.map((m) => {
-                  const name = ((m.display_name || "").trim() || (m.email || "").trim() || "—");
-                  return (
-                    <div
-                      key={m.id}
-                      style={{
-                        padding: "6px 10px",
-                        borderRadius: 999,
-                        border: `1px solid rgba(233,216,166,0.18)`,
-                        background: "rgba(10,10,12,0.35)",
-                        color: stylesTokens.textMain,
-                        fontSize: 13,
-                        fontWeight: 900,
-                      }}
-                    >
-                      {name}
-                    </div>
-                  );
-                })}
-              </div>
-            </div>
-          )}
-
 
           {/* ✅ CHOICE: nur wenn Spiel beendet oder kein Spiel selected */}
           {mode === "choice" && (