Add Playwright E2E testing infrastructure

- New apps/e2e workspace with @playwright/test
- playwright.config.ts targeting Docker Compose stack (http://localhost:8080)
- navigation.spec.ts: smoke tests for all pages
- book.spec.ts: full booking wizard happy-path with API mocking
- clients.spec.ts: client list and detail panel tests
- CI job: spins up docker compose, installs Playwright chromium, runs tests
- Playwright report uploaded as artifact on failure
- README docs for running E2E tests locally

Closes #40

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/e2e/tests/clients.spec.ts

@@ -0,0 +1,59 @@
+import { test, expect } from "@playwright/test";
+
+/**
+ * Client management E2E tests.
+ *
+ * API calls are mocked so tests run without a live backend.
+ */
+
+const MOCK_CLIENTS = [
+  {
+    id: "client-1",
+    name: "Alice Johnson",
+    email: "alice@example.com",
+    phone: "555-0101",
+    address: null,
+    notes: null,
+    createdAt: "2026-01-01T00:00:00.000Z",
+    updatedAt: "2026-01-01T00:00:00.000Z",
+  },
+  {
+    id: "client-2",
+    name: "Bob Williams",
+    email: "bob@example.com",
+    phone: null,
+    address: null,
+    notes: null,
+    createdAt: "2026-01-02T00:00:00.000Z",
+    updatedAt: "2026-01-02T00:00:00.000Z",
+  },
+];
+
+test.beforeEach(async ({ page }) => {
+  await page.route("/api/clients**", (route) =>
+    route.fulfill({ json: MOCK_CLIENTS })
+  );
+  // Pets loaded when a client is selected
+  await page.route("/api/clients/*/pets", (route) =>
+    route.fulfill({ json: [] })
+  );
+});
+
+test("clients page shows client list", async ({ page }) => {
+  await page.goto("/clients");
+  await expect(page.getByText("Alice Johnson")).toBeVisible();
+  await expect(page.getByText("Bob Williams")).toBeVisible();
+});
+
+test("clients page shows search input", async ({ page }) => {
+  await page.goto("/clients");
+  await expect(page.getByPlaceholder(/search/i)).toBeVisible();
+});
+
+test("clicking a client shows their details", async ({ page }) => {
+  await page.goto("/clients");
+  await expect(page.getByText("Alice Johnson")).toBeVisible();
+  await page.getByText("Alice Johnson").click();
+  // Client detail panel shows their email
+  await expect(page.getByText("alice@example.com")).toBeVisible();
+});