Amazingly, that was the second fail after I upgraded my work machine to Sequioa. Initially I was greeted by this screen – I didn’t bother making a video, because you couldn’t have seen anything. Literally nothing was clickable: Not the More… links, not the checkbox, not the Cancel button. Nothing in the background window either, of course. I clicked and double-clicked on everything like a madman. I tried Enter, Space, Esc… nothing. I had to force-quit System Settings, and then I ran into the issue in the video above.
I was only able to proceed with both actions after a reboot.