How to completely remove old school account

So I'm trying to get rid of my old school account in preparation to add my new (currently unpaid) personal account. The problem is, it's been several months since I graduated from my previous school, and my account there has since been terminated. The desktop app, however, doesn't seem to know that's happened, as whenever I try to open the desktop app, it tells me that I've been signed out, and that I need to sign in again. However, when I click the button to do that, it will simply lead me back to the same window, and this repeats ad infinitum. My hypothesis is that the desktop app is attempting to automatically sign in to an account which no longer exists. Is this what's happening, and is there any way to fix/bypass the issue?