Is it possible, when hosted by Discourse, to customize the forums so that the badges show up next to the user avatar? Envato has done it as seen here: Screenshot - 35a3b0817ba1db69cd53bec2213fdb1e - Gyazo but Im not sure if they had to host somewhere else so that they could edit the template files.
This kind of change requires a custom plugin. If you have a budget for it make a post in #marketplace place.
It is not simply “editing a file” the information needs to be supplied from the server so this requires a custom plugin.
If this requires a custom plugin this means that we can’t actually obtain this if we go with Discourse’s own business tier hosting?
That is correct. Custom plugins require an Enterprise plan.
Compared to plugins it would be limited in what could be done, but for some things it might be enough.
Yes. Any plan allows that.