feat: live game tiles on homepage + bot spectating

- GET /v1/games/live returns all active games with both players assigned,
  including current FEN (computed server-side via chess.js)
- LiveGames component on homepage: mini chessboard tiles (160px) that
  auto-refresh every 3s, clickable to join as spectator
- Tournament page: 'Zuschauen' button for non-players on ongoing rounds
  (bot vs bot, human vs human, human vs bot all spectatable)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

client/src/components/home/LiveGames.tsx

@@ -0,0 +1,51 @@
+"use client";
+
+import { useEffect, useState } from "react";
+import { Chessboard } from "react-chessboard";
+import Link from "next/link";
+import { fetchLiveGames, type LiveGameEntry } from "@/lib/game";
+
+export default function LiveGames() {
+  const [games, setGames] = useState<LiveGameEntry[]>([]);
+
+  useEffect(() => {
+    let mounted = true;
+    const load = async () => {
+      const data = await fetchLiveGames();
+      if (mounted) setGames(data);
+    };
+    load();
+    const interval = setInterval(load, 3000);
+    return () => { mounted = false; clearInterval(interval); };
+  }, []);
+
+  if (!games.length) return null;
+
+  return (
+    <div>
+      <h2 className="text-xl font-bold mb-3">Laufende Partien</h2>
+      <div className="grid grid-cols-2 sm:grid-cols-3 lg:grid-cols-4 xl:grid-cols-5 gap-3">
+        {games.map((game) => (
+          <Link
+            key={game.code}
+            href={`/${game.code}`}
+            className="card bg-base-200 hover:bg-base-300 transition-colors overflow-hidden"
+          >
+            <Chessboard
+              position={game.fen}
+              boardWidth={160}
+              arePiecesDraggable={false}
+              customDarkSquareStyle={{ backgroundColor: "#4b7399" }}
+              customLightSquareStyle={{ backgroundColor: "#eae9d2" }}
+            />
+            <div className="px-2 py-1.5 flex flex-col gap-0.5">
+              <span className="text-xs font-semibold truncate">{game.black?.name}</span>
+              <span className="text-xs opacity-40 text-center leading-none">vs</span>
+              <span className="text-xs font-semibold truncate">{game.white?.name}</span>
+            </div>
+          </Link>
+        ))}
+      </div>
+    </div>
+  );
+}