feat(bots): add named bot profiles with ELO-based difficulty

- 5 bot profiles (Holzpferd Heinz to Meister Magnus, ELO 200-1400) in
  server/bots.ts and client/bots.ts with emoji + descriptions
- Bot users auto-created in DB on server startup (role='bot')
- AI page replaced difficulty buttons with bot profile cards
- Tournament host can add bots via dropdown (POST /:code/add-bot)
- Bot auto-moves triggered on joinLobby and after each human move
- Fixed clock start order so bot-as-white games initialize correctly

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

server/src/controllers/tournament.controller.ts

@@ -1,6 +1,7 @@
 import type { Request, Response } from "express";
 import TournamentModel from "../db/models/tournament.model.js";
 import { activeGames } from "../db/models/game.model.js";
+import { db } from "../db/index.js";
 import { nanoid } from "nanoid";
 import type { Game } from "@michess/types";
 
@@ -80,3 +81,22 @@ export const startTournament = async (req: Request, res: Response) => {
         res.status(200).json(updated);
     } catch (e) { console.error(e); res.status(500).end(); }
 };
+
+export const addBot = async (req: Request, res: Response) => {
+    if (!req.session.user?.id || typeof req.session.user.id === "string") { res.status(401).end(); return; }
+    const { botName } = req.body;
+    if (!botName) { res.status(400).json({ message: "Bot name erforderlich." }); return; }
+    try {
+        const tournament = await TournamentModel.findByCode(req.params.code);
+        if (!tournament) { res.status(404).end(); return; }
+        if (tournament.hostId !== req.session.user.id) { res.status(403).end(); return; }
+        if (tournament.status !== "waiting") { res.status(400).json({ message: "Turnier bereits gestartet." }); return; }
+        const botRes = await db.query(`SELECT id, name FROM "user" WHERE name=$1 AND role='bot'`, [botName]);
+        if (!botRes.rows[0]) { res.status(404).json({ message: "Bot nicht gefunden." }); return; }
+        const bot = botRes.rows[0];
+        const result = await TournamentModel.joinTournament(req.params.code, bot.id, bot.name);
+        if (!result) { res.status(400).json({ message: "Bot konnte nicht hinzugefügt werden." }); return; }
+        const updated = await TournamentModel.findByCode(req.params.code);
+        res.status(200).json(updated);
+    } catch (e) { console.error(e); res.status(500).end(); }
+};