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>

server/src/controllers/games.controller.ts

@@ -1,9 +1,28 @@
 import type { Game, User } from "@michess/types";
 import type { Request, Response } from "express";
 import { nanoid } from "nanoid";
+import { Chess } from "chess.js";
 
 import GameModel, { activeGames } from "../db/models/game.model.js";
 
+export const getLiveGames = (_req: Request, res: Response) => {
+    const live = activeGames
+        .filter(g => g.white?.id && g.black?.id && !g.winner)
+        .map(g => {
+            const chess = new Chess();
+            if (g.pgn) chess.loadPgn(g.pgn);
+            return {
+                code: g.code,
+                white: { name: g.white?.name },
+                black: { name: g.black?.name },
+                fen: chess.fen(),
+                timeControl: g.timeControl,
+                tournamentCode: g.tournamentCode
+            };
+        });
+    res.status(200).json(live);
+};
+
 export const getGames = async (req: Request, res: Response) => {
     try {
         if (!req.query.id && !req.query.userid) {

server/src/routes/games.route.ts

@@ -4,6 +4,7 @@ import * as controller from "../controllers/games.controller.js";
 
 const router = Router();
 
+router.get("/live", controller.getLiveGames);
 router.route("/").get(controller.getGames).post(controller.createGame);
 
 router.route("/:code").get(controller.getActiveGame);