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/pages/AccountMenu.ts

@@ -0,0 +1,18 @@
+import { type Page } from '@playwright/test';
+import { BasePage, waitForVisible } from '@levkin/playkit';
+
+export class AccountMenu extends BasePage {
+  constructor(page: Page, baseUrl: string) {
+    super(page, baseUrl);
+  }
+
+  async openMenu(): Promise<void> {
+    await this.click(this.page.getByLabel('Account menu'));
+    await waitForVisible(this.page.getByRole('button', { name: 'Sign out' }));
+  }
+
+  async signOut(): Promise<void> {
+    await this.openMenu();
+    await this.click(this.page.getByRole('button', { name: 'Sign out' }));
+  }
+}

e2e/pages/LoginPage.ts

@@ -0,0 +1,18 @@
+import { type Page } from '@playwright/test';
+import { BasePage } from '@levkin/playkit';
+
+export class LoginPage extends BasePage {
+  constructor(page: Page, baseUrl: string) {
+    super(page, baseUrl);
+  }
+
+  async openLogin(): Promise<void> {
+    await this.open('/login');
+  }
+
+  async signIn(email: string, password: string): Promise<void> {
+    await this.fill(this.page.locator('#email'), email);
+    await this.fill(this.page.locator('#password'), password);
+    await this.click(this.page.locator('button[type="submit"]'));
+  }
+}