chore: rename playwrite to playwright (#1203)

I assume this was a mistake and not intentional.

playwright-tests/fullstack.spec.js

@@ -0,0 +1,32 @@
+// @ts-check
+const { test, expect } = require('@playwright/test');
+
+test('button click', async ({ page }) => {
+  await page.goto('http://localhost:3333');
+
+  // Expect the page to contain the counter text.
+  const main = page.locator('#main');
+  await expect(main).toContainText('hello axum! 12345');
+
+  // Click the increment button.
+  let button = await page.locator('button.increment-button');
+  await button.click();
+
+  // Expect the page to contain the updated counter text.
+  await expect(main).toContainText('hello axum! 12346');
+});
+
+test('fullstack communication', async ({ page }) => {
+  await page.goto('http://localhost:3333');
+
+  // Expect the page to contain the counter text.
+  const main = page.locator('#main');
+  await expect(main).toContainText('Server said: ...');
+
+  // Click the increment button.
+  let button = await page.locator('button.server-button');
+  await button.click();
+
+  // Expect the page to contain the updated counter text.
+  await expect(main).toContainText('Server said: Hello from the server!');
+});