When I sign up, it texts me the code, I enter the code and click "Next" it asks "Which account do you want to sign out of?", and actually displays no accounts. Why ? I don't want to sign out. I want to sign UP!
Does your university 365 account have a Office 365 subscription/license already?
If your university 365 account have a Office 365 subscription/license (e.g. Office 365 Education A1, Office 365 Education A2, etc) already, I think you may not be necessary to sign up for PowerApps, you could sign in PowerApps directly.
Some Office 365 subscriptions also include PowerApps license. More details about PowerApps for Office 365, please check the following article: