I have a wrist issue that prohibits me from using the mouse for long periods of time. I heard shadowlands had controller support now, however, the website says mouse and keyboard only. Can I use a controller without the use of 3rd party programs?

I haven't played for a while but I know it is possible. It used to be done through an addon, console port (maybe ConsolePort). There are a few other ways to do it. They did add the infrastructure for controller support but didn't activate it.