But I can’t find the host url and I can’t find any docs on where to get it. I do see some that suggest I can only use the default branch for free but can I also not get this information?
If you’re using SonarQube Cloud you don’t need to set the SONAR_HOST_URL, this action already sets it by default to the URL of SonarQube Cloud. Here’s the relevant documentation: Github Actions | SonarQube Cloud Documentation
But to be honest, it is highly recommended to thoroughly review the documentation. There is a lot of important information available on other pages.