Can repro. The radio buttons do not appear in the banner, and it appears that interaction with the poll is not considered an edit, and thus not picked up by the banner.
Using polls in banners is a cool idea! But I’m not surprised it doesn’t work and I’d say it’s not necessarily a bug… it’s not really how polls are designed to be used. So… “don’t do that”.
Or maybe this topic can be made a feature request. I can see it being a pretty neat feature!