Playwright does use "real" web browsers (Chromium, Firefox, WebKit). It just supports specific versions, as otherwise it would be difficult to maintain. It runs them in headless mode, which most browsers support, and should behave exactly as a headed version would. You can start a test in headed mode if you want to see the browser window.

The era of custom headless browsers like PhantomJS, or Selenium/WebDriver for that matter, is dead, IMO. The Chrome DevTools Protocol is the modern standard API to interact with a browser programmatically.