So, after working on this for a while - and NOT reinstalling Windows (that's insane) or Office (also insane) - I was able to get it to work again. This is what worked for me:
- Hit Windows key + R
- Type "services.msc" and press Enter
- Find "Microsoft Account Sign-in Assistant" in the list. Right-click and select "Restart."
- Find "Microsoft Cloud Identity Service" in the list. Right-click and select "Restart."
- Open Word, Excel, PPT, or whatever and try to sign in again. Worked immediately for me.
Quick note to the Microsoft employees and advisors trying to "help" here: Please work to provide help, real assistance, rather than a simple-yet-insanely-un-fun solution like "Just reinstall the OS." That is not a solution.