Ah hah! Figured it out: some cosmetic filter is killing the dropdowns. Unfortunately the effecting rule is not discernable in the dev tools, so figuring out which rule is at fault is tricky and slow.

Found which one, too: it was a rule of my own that I added almost a year ago to kill off some of the annoying cards they pop up at the ends of many videos, which hide the video content; turns out my rule was just a touch too broad for how they do things.

Mea culpa.