Fix double /api prefix causing invite gate bypass and broken API calls

VITE_API_URL was /api but all API paths already included /api/,
resulting in /api/api/config etc. Config call failed silently and
defaulted to requireInvite:false. Set VITE_API_URL to empty string
so paths like /api/auth/anonymous go through nginx as-is.

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

apps/web/src/lib/api.ts

@@ -112,7 +112,7 @@ export function validateStoredToken(): void {
 }
 
 export const api = {
-  health: () => request<{ status: string }>('/health', { timeoutMs: 5_000 }),
+  health: () => request<{ status: string }>('/api/health', { timeoutMs: 5_000 }),
   auth: {
     anonymous: () => request<{ userId: string; token: string }>('/api/auth/anonymous', { method: 'POST' }),
     login: (login: string, password: string) =>