feat: add Playwright E2E testing framework

Add @playwright/test, playwright.config.ts, e2e/ smoke test,
and e2e CI job (Chromium-only) that gates build-and-push.

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

playwright.config.ts

@@ -0,0 +1,19 @@
+import { defineConfig, devices } from '@playwright/test';
+
+export default defineConfig({
+  testDir: './e2e',
+  projects: [
+    {
+      name: 'chromium',
+      use: { ...devices['Desktop Chrome'] },
+    },
+  ],
+  webServer: {
+    command: 'npm run dev',
+    url: 'http://localhost:5173',
+    reuseExistingServer: !process.env.CI,
+  },
+  use: {
+    baseURL: 'http://localhost:5173',
+  },
+});