From my quick tests (because I got curious 
), if you use a CSS snippet to de-alias/add the “missing” GitHub callouts in Obsidian, Obsidian will render the callouts in that modal as you would like them to… At least, for the colors 
… I sadly couldn’t make it work for the icon 
…
If I enable the CSS snippet I shared in this feature request → Support all five types of GitHub admonitions/alerts - #4 by Pch (which could be updated, now that Obsidian uses a more recent version of the Lucide icon library) … and then look for the plugin Badges, for example, in the Community plugins store, I get the following Important callout rendered:
… as opposed to this rendering, when the CSS snippet is disabled 
:
I really have no clue for the missing icon though 
(I’m no CSS magician ) … and I didn’t had the opportunity to dig into this further 