feat: add Playwright E2E test config and basic tests

Adds playwright.config.ts pointing at tests/e2e/ with a 15s timeout and dev server reuse. Stubs two test files: public-pages (home, pets, login load checks) and admin-guard (unauthenticated /admin and /foster redirect to /login). Installs @playwright/test as a dev dependency.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

tests/e2e/public-pages.test.ts

@@ -0,0 +1,16 @@
+import { test, expect } from '@playwright/test';
+
+test('home page loads', async ({ page }) => {
+	await page.goto('/');
+	await expect(page).toHaveTitle(/./);
+});
+
+test('pets page loads', async ({ page }) => {
+	await page.goto('/pets');
+	await expect(page.locator('h1')).toBeVisible();
+});
+
+test('login page loads', async ({ page }) => {
+	await page.goto('/login');
+	await expect(page.locator('form')).toBeVisible();
+});