test: add Playwright e2e smoke suite for punimtag dev

Add an e2e/ Playwright harness (via @levkin/playkit) that smoke-tests
the public DEV host: login page loads, sign-out never redirects to a
LAN host, FastAPI /health responds, and forgot-password mail lands in
Mailtrap with a public reset link (Kolby #56/#57 regressions).

Wire it into Gitea Actions as a new `e2e` job (self-hosted runner,
Chromium via Playwright), gated behind the existing skip-ci-check.
Add npm root scripts (install:e2e, test:e2e) and gitignore e2e build
artifacts (node_modules, reports, .env).

e2e/tests/api.health.spec.ts

@@ -0,0 +1,10 @@
+import { test, expect } from '../fixtures';
+
+test.describe('api @smoke', () => {
+  test('backend /health returns ok', async ({ api, timings }) => {
+    const res = await timings.measure('api_health', () =>
+      api.get<{ status: string }>('/health', { expectedStatus: 200 }),
+    );
+    expect(res.data).toMatchObject({ status: 'ok' });
+  });
+});