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>

client/src/app/tournament/[code]/page.tsx

@@ -2,7 +2,8 @@
 
 import InviteFriendsModal from "@/components/InviteFriendsModal";
 import { useSession } from "@/context/session";
-import { fetchTournament, joinTournament, startTournament } from "@/lib/tournament";
+import { fetchTournament, joinTournament, startTournament, addBotToTournament } from "@/lib/tournament";
+import { BOTS } from "@/bots";
 import type { Tournament, TournamentRound } from "@michess/types";
 import Link from "next/link";
 import { useParams } from "next/navigation";
@@ -16,6 +17,7 @@ export default function TournamentDetailPage() {
   const [tournament, setTournament] = useState<Tournament | null>(null);
   const [loading, setLoading] = useState(true);
   const [actionLoading, setActionLoading] = useState(false);
+  const [selectedBot, setSelectedBot] = useState(BOTS[0].name);
   const intervalRef = useRef<ReturnType<typeof setInterval> | null>(null);
 
   async function load() {
@@ -47,6 +49,13 @@ export default function TournamentDetailPage() {
     setActionLoading(false);
   }
 
+  async function handleAddBot() {
+    setActionLoading(true);
+    const updated = await addBotToTournament(code, selectedBot);
+    if (updated) setTournament(updated);
+    setActionLoading(false);
+  }
+
   async function handleStart() {
     if (!user?.id) return;
     setActionLoading(true);
@@ -123,6 +132,27 @@ export default function TournamentDetailPage() {
           {tournament.status === "waiting" && isJoined && (
             <InviteFriendsModal gameCode={`tournament/${code}`} label="Freunde einladen" />
           )}
+          {isHost && tournament.status === "waiting" && (
+            <div className="flex gap-2 items-center">
+              <select
+                className="select select-sm select-bordered"
+                value={selectedBot}
+                onChange={(e) => setSelectedBot(e.target.value)}
+                disabled={actionLoading}
+              >
+                {BOTS.map((b) => (
+                  <option key={b.name} value={b.name}>{b.emoji} {b.name} ({b.elo})</option>
+                ))}
+              </select>
+              <button
+                className={"btn btn-outline btn-sm" + (actionLoading ? " loading" : "")}
+                onClick={handleAddBot}
+                disabled={actionLoading}
+              >
+                Bot hinzufügen
+              </button>
+            </div>
+          )}
           {canStart && (
             <button
               className={"btn btn-primary btn-sm" + (actionLoading ? " loading" : "")}