Fix proxy path — prepend /api/ when forwarding to FastAPI

app/api/[...slug]/route.ts

@@ -7,7 +7,7 @@ async function handler(
   { params }: { params: Promise<{ slug: string[] }> }
 ) {
   const { slug } = await params;
-  const path = '/' + slug.join('/');
+  const path = '/api/' + slug.join('/');
   const url = `${API_BASE}${path}${request.nextUrl.search}`;
 
   const headers = new Headers();