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/vitest.config.ts

@@ -0,0 +1,14 @@
+import { defineConfig } from "vitest/config";
+import react from "@vitejs/plugin-react";
+import { resolve } from "node:path";
+
+export default defineConfig({
+    plugins: [react()],
+    resolve: { alias: { "@": resolve(__dirname, ".") } },
+    test: {
+        environment: "jsdom",
+        globals: true,
+        setupFiles: ["./test/setup.ts"],
+        include: ["**/*.test.{ts,tsx}"],
+    },
+});