We have a couple of options on how to do this. We'll probably have to come to a standardized way of attaching any sort of action to a card. We have some examples in the wild, like Hovercards, with its setting ButtonWidget (with icon only), and MessageDialog in OOUI. A floating green round button is pretty much an alien :)

Hovercards	MessageDialog	Round green alien

Between the Hovercards and the MessageDialog options, the latter might be clearer. We are already using a similar pattern on the Wikidata item annotations. Also, I fear that the Hovercards way might not make it clear what the user is editing (is it the Wikidata description, or the annotation itself. better placement will improve understanding, but I am not sure where that would be).

Hovercards	MessageDialog

In T154752#2927623, @Prtksxna wrote:

Between the Hovercards and the MessageDialog options, the latter might be clearer. We are already using a similar pattern on the Wikidata item annotations. Also, I fear that the Hovercards way might not make it clear what the user is editing (is it the Wikidata description, or the annotation itself. better placement will improve understanding, but I am not sure where that would be).

I think it makes sense to make editing to be less prominent than the main actions to access information. Maybe using just the icon may be enough. In terms of placement, at the right of the title (next to the right edge of the card) could work well in terms of feeling as a global but non prominent action.