"Save as..." bug in Monterey 12.0.1?

I upgraded from Big Sur to Monterey (12.0.1) this week and worked on a presentation in Keynote (version 11.2). Much to my surprise, whenever I try to save the presentation under a different name using "Save As..." or export it to PDF or Powerpoint using "Export", it either never provides a save dialog box or hangs with the spinning beachball.

Now while you might think this is a Keynote issue, the same behavior is also exhibited by Pages, Numbers, and even the venerable Microsoft Word. Interestingly, applications that save just plain text like TextEdit seem to work fine when I invoked "Save As...". This makes me think this is an OS and not application problem.

I've tried deleting and reinstalling Keynote, reverting Keynote to an earlier version (it updated this week along with Monterey), and I've also completely reinstalled Monterey from scratch. The behavior still persists.

Any ideas what might be the issue here? I'm hoping that the new Monterey 12.1 might fix this, but I'd rather not install the beta until it's released.

-C