chore: improve production deployment flexibility

- Switch frontend from nginx to caddy for consistency with Coolify
- Make VITE_API_URL optional, auto-derive from window.location.origin/api
- Simplifies deployment by not requiring build-time API URL

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/src/api/client.ts

@@ -1,4 +1,5 @@
-const API_URL = import.meta.env.VITE_API_URL || 'http://localhost:8000';
+// Use VITE_API_URL if set at build time, otherwise derive from current origin
+const API_URL = import.meta.env.VITE_API_URL || `${window.location.origin}/api`;
 
 export interface ParticipantAPI {
   id: string;