fix: add missing DELETE export to catch-all route

Next.js [...path] route only exported GET/POST/PUT, causing all DELETE
requests (including deck deletion) to be silently rejected before
reaching the router. Deck delete was impossible.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/src/app/api/[...path]/route.ts

@@ -26,3 +26,7 @@ export async function POST(request: NextRequest, { params }: { params: { path: s
 export async function PUT(request: NextRequest, { params }: { params: { path: string[] } }) {
   return dispatch(request, params.path, 'PUT');
 }
+
+export async function DELETE(request: NextRequest, { params }: { params: { path: string[] } }) {
+  return dispatch(request, params.path, 'DELETE');
+}