feat(adminsite): test harness, typed client and the not-connected state

The repo's first frontend test setup: Vitest, React Testing Library, jsdom.
Scoped to the flows that lose money or leak data when broken, per spec 4.

lib/api.ts collapses every failure into three the UI can act on:
NotConnected (unreachable, or no URL baked in), ApiError 401 (redirect), and
ApiError with the backend's own message, which is customer-facing and shown
verbatim rather than replaced with something vaguer.

The not-connected panel names the variable, the value baked in, and both
reasons it fails -- unreachable from the browser, or missing from admin's
ADMIN_ORIGIN. Proven by test before it existed.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

adminsite/lib/query-client.ts

@@ -0,0 +1,16 @@
+"use client";
+
+import { QueryClient } from "@tanstack/react-query";
+import { ApiError, NotConnected } from "./api";
+
+export const queryClient = new QueryClient({
+    defaultOptions: {
+        queries: {
+            staleTime: 30_000,
+            // Retrying a 401 or a missing API URL just delays the redirect and
+            // the not-connected panel.
+            retry: (count, error) =>
+                error instanceof NotConnected || error instanceof ApiError ? false : count < 1,
+        },
+    },
+});