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/playwright.config.ts

@@ -0,0 +1,33 @@
+import { defineConfig, devices } from "@playwright/test";
+
+/**
+ * Playwright configuration for Groom Book E2E tests.
+ *
+ * Targets the Docker Compose stack:
+ *   - Web:  http://localhost:8080
+ *   - API:  http://localhost:3000 (proxied via the web container's nginx)
+ *
+ * Run locally:
+ *   docker compose up -d
+ *   pnpm --filter @groombook/e2e test
+ */
+export default defineConfig({
+  testDir: "./tests",
+  timeout: 30_000,
+  retries: process.env.CI ? 2 : 0,
+  workers: process.env.CI ? 1 : undefined,
+  reporter: process.env.CI ? "github" : "list",
+
+  use: {
+    baseURL: "http://localhost:8080",
+    trace: "on-first-retry",
+    screenshot: "only-on-failure",
+  },
+
+  projects: [
+    {
+      name: "chromium",
+      use: { ...devices["Desktop Chrome"] },
+    },
+  ],
+});