chore: add Playwright test scaffolding

Adds @playwright/test and @types/node as dev dependencies, playwright.config.ts
with a localhost:1420 base URL targeting the Vite dev server, an example
spec, and the standard Playwright output directories to .gitignore.

tests/example.spec.ts

@@ -0,0 +1,18 @@
+import { test, expect } from '@playwright/test';
+
+test('has title', async ({ page }) => {
+  await page.goto('https://playwright.dev/');
+
+  // Expect a title "to contain" a substring.
+  await expect(page).toHaveTitle(/Playwright/);
+});
+
+test('get started link', async ({ page }) => {
+  await page.goto('https://playwright.dev/');
+
+  // Click the get started link.
+  await page.getByRole('link', { name: 'Get started' }).click();
+
+  // Expects page to have a heading with the name of Installation.
+  await expect(page.getByRole('heading', { name: 'Installation' })).toBeVisible();
+});