The App Store app is logged out, and logging in with the correct credentials spins for a moment then leaves the app without being logged in.
As of now I'm suspecting a filesystem issue, perhaps permissioning, as I've seen other things that might point that way.
Anyone else seeing this?
All preference panes requiring authentication fail for me, so the solution of logging out of iCloud through Preferences didn't work for me.
What did work was logging out of the Music app, logging back into the Music app, then logging into App Store.
Hope this (or the Preferences variant) helps others.