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>

types/index.d.ts

@@ -27,6 +27,7 @@ export interface User {
     wins?: number;
     losses?: number;
     draws?: number;
+    elo?: number;
     role?: "user" | "admin";
 
     // mainly for players, not spectators