Do you know why this is needed now? I think a while ago it was possible to select new icons for badges without adding them to the site setting (with a quick search, I only found a PR adding the parameter to only show available icons in the icon picker for sidebar links, because users aren’t able to add new icons, which indicates that in other places this was possible).
Discourse offered all the icons available on FontAwesome in search, which is really helpful because otherwise there is no way to learn about the icons in Discourse. It doesn’t seem to match the strategy of making things easier to set up if you now need to search on FontAwesome.com, add the icon to a site setting, and add it to a badge instead of searching and selecting it in the icon picker.
And in this case it would have helped avoid the struggle of using the correct prefix.