test: Add with_response overload tests (#10685)

test: add overload tests

Co-authored-by: kodiakhq[bot] <49736102+kodiakhq[bot]@users.noreply.github.com>

vitest.d.ts

@@ -0,0 +1,8 @@
+/* eslint-disable @typescript-eslint/no-empty-interface */
+// This file only exists because of https://github.com/vitejs/vite/issues/9813.
+declare interface Worker {}
+declare interface WebSocket {}
+
+declare namespace WebAssembly {
+	interface Module {}
+}