Real-browser tests (Playwright) and housekeeping

- npm run test:e2e builds the app, runs it on port 3101 with an empty throwaway
  database and drives Chrome (the installed one; no browser download) through
  notes and the paste check, the daily five minutes and weekly recall,
  translation compare (Bible text faked), and two-screen presenting.
- Vitest skips e2e/; ESLint knows the e2e folder and playwright.config.js.
- .gitignore: the local demo video, Playwright output and sign-in file.
- README and TODO describe the browser tests and what CI still needs.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

e2e/auth.setup.js

@@ -0,0 +1,12 @@
+// Makes one account in the throwaway database and keeps its sign-in for the other tests.
+import { test as setup, expect } from '@playwright/test';
+
+setup('create an account and sign in', async ({ page }) => {
+  await page.goto('/');
+  await page.getByRole('button', { name: /need an account\? sign up/i }).click();
+  await page.locator('input[type="email"]').fill('e2e@example.test');
+  await page.locator('input[type="password"]').fill('E2e-Test-Password-7391');
+  await page.getByRole('button', { name: 'Create account' }).click();
+  await expect(page.getByRole('heading', { name: 'My Studies' })).toBeVisible();
+  await page.context().storageState({ path: 'e2e/.auth.json' });
+});