Thanks goodness, I'm not the only one experiencing this.
I too run the App Store version of Outlook. I have no other Office products installed (I use Libreoffice). So, when "updating" it yesterday I was locked out of being online.
Click on the "go online" button and it brings up a window that compares my free plan to the 365 packages. And even then I can't do anything.
I've left a review in the App Store giving it one star and a description of the problem.
Meanwhile I'm using Apple's Mail and Calendar apps which are connected to my MS account. They work but they're not as easy or as useful as having it all in the one place. Plus, I miss my categories for calendar entries (they all have different colors so specific types of calendar entries stick out from each other.
I have the previous version running on my Macbook Air and that'll stay that way til this is fixed. And if it isn't, then I'll migrate everything over to Gmail and close my Outlook account.