feat(elo): add ELO rating system

- DB: elo column on user table (default 1200, added via ALTER TABLE IF NOT EXISTS)
- ELO calculated after every game save (K=32, min 100)
- Bots use their fixed ELO values; only human players' ELO changes
- AI page games save with bot name (e.g. 'Holzpferd Heinz') instead of 'Stockfish'
- User profile shows ELO badge below name
- Header shows current ELO for logged-in users (links to profile)

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

client/src/app/ai/page.tsx

@@ -42,7 +42,7 @@ export default function AiGamePage() {
         method: "POST",
         credentials: "include",
         headers: { "Content-Type": "application/json" },
-        body: JSON.stringify({ pgn: g.pgn(), winner, endReason, playerColor: color, level, startedAt: startedAtRef.current })
+        body: JSON.stringify({ pgn: g.pgn(), winner, endReason, playerColor: color, level, botName: selectedBot.name, startedAt: startedAtRef.current })
       });
       if (res.ok) {
         const { id } = await res.json();

client/src/app/user/[name]/page.tsx

@@ -43,7 +43,12 @@ export default async function Profile({ params }: { params: { name: string } })
   return (
     <div className="mt-8 flex w-full flex-col gap-8">
       <div className="flex flex-wrap items-center justify-between gap-4 md:gap-8">
-        <h1 className="text-4xl font-bold">{data.name}</h1>
+        <div>
+          <h1 className="text-4xl font-bold">{data.name}</h1>
+          {data.elo != null && (
+            <span className="badge badge-primary badge-lg mt-1 font-mono">{data.elo} ELO</span>
+          )}
+        </div>
         <div className="flex gap-6">
           <div className="flex flex-col items-center">
             <span className="text-sm">Wins</span>

client/src/components/Header.tsx

@@ -37,6 +37,11 @@ export default function Header() {
           </Link>
         )}
         {user?.id && typeof user.id === "number" && <NotificationPanel />}
+        {user?.elo != null && typeof user.id === "number" && (
+          <Link href={`/user/${user.name}`} className="btn btn-ghost btn-sm font-mono tabular-nums" title="Deine ELO-Wertung">
+            {user.elo}
+          </Link>
+        )}
         <ThemeToggle />
         <label tabIndex={0} htmlFor="auth-modal" className="btn btn-ghost btn-circle avatar">
           <div className="w-10 rounded-full">