@V-FRROME Thanks for your help, but none of those suggestions work.
I've already tried all of those settings, but if I stay logged into Edge, I am automatically logged into OneDrive - even after I've manually cleared all cookies. This is unacceptable behavior for a browser for me.
This is precisely why I hated logging into Chrome because I did not want to automatically log into every Google service automatically. MS seems to have aped this behavior.
An option to log out of the browser would suffice. For now, I'll stick to Firefox because it is a seperate account from both my MS and Google accounts.