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/components/NotConnected.test.tsx

@@ -0,0 +1,23 @@
+import { render, screen } from "@testing-library/react";
+import { describe, expect, it } from "vitest";
+import { NotConnectedPanel } from "./NotConnected";
+
+describe("NotConnectedPanel", () => {
+    it("names the variable that is wrong and where it is set", () => {
+        render(<NotConnectedPanel url="https://admin.example.com" />);
+
+        expect(screen.getByRole("heading")).toHaveTextContent(
+            /not connected to the licensing service/i,
+        );
+        expect(screen.getByText(/ADMIN_API_URL/)).toBeInTheDocument();
+        expect(screen.getByText(/https:\/\/admin\.example\.com/)).toBeInTheDocument();
+        // The two mistakes that actually cause this, both named.
+        expect(screen.getByText(/reachable from your browser/i)).toBeInTheDocument();
+        expect(screen.getByText(/ADMIN_ORIGIN/)).toBeInTheDocument();
+    });
+
+    it("says the value is missing when no URL was baked in", () => {
+        render(<NotConnectedPanel url="" />);
+        expect(screen.getByText(/was not set when this app was built/i)).toBeInTheDocument();
+    });
+});