The attacker can do anything using your session.

The "Hello world" examples always show using it to steal your cookies, which obviously doesn't work now when nearly every site uses the "httpOnly" flag which makes the cookie inaccessible to JavaScript, but really, stealing your session isn't necessary. They just have to make the XSS payload run the necessary JavaScript.

Once the JavaScript is running on the page, all bets are off. They can do ANYTHING that the page can do, because now they can make HTTP requests on your behalf. SOP no longer applies. CSRF no longer protects you. The attacker has full control of your account, and all the requests will appear to come from YOUR browser.