Unable to connect from TV12 on Mac; empty computers list after TV13 upgrade

I was having problems with TeamViewer 12 on Mac OS, where I could only connect anymore by logging into the web interface and clicking a link for one of my computers, which was then opened by the TeamViewer app.

Today that stopped working; the TeamViewer 12 client gave no error or other indication, but simply wouldn't show any sign of trying to connect.

I installed TeamViewer 13. My computers list is now empty. When I manually paste in the ID of a computer I want to connect to, it does nothing. When I click a "connect" link in the web interface, I get an error that I'm trying to connect to the same machine (I double checked that this isn't true).

I have no trouble with my computer list or making connections from another machine that is running Linux and Teamviewer 12.0.

How do I get a working Teamviewer client on Mac OS?