[CHORE] Add playwright eslint plugin

- Add https://github.com/playwright-community/eslint-plugin-playwright
as a linter for the playwright tests.
- `no-networkidle` and `no-conditional-in-test` are disabled as fixing
those doesn't seem to really improve testing quality for our use case.
- Some non-recommended linters are enabled to ensure consistency (the
prefer rules).

tests/e2e/profile_actions.test.e2e.js

@@ -27,7 +27,7 @@ test('Follow actions', async ({browser}, workerInfo) => {
   await expect(page.locator('#block-user')).toBeVisible();
   await page.locator('#block-user .ok').click();
   await expect(page.locator('.block')).toContainText('Unblock');
-  await expect(page.locator('#block-user')).not.toBeVisible();
+  await expect(page.locator('#block-user')).toBeHidden();
 
   // Check that following the user yields in a error being shown.
   await followButton.click();