ULS looks and works great for me, after trying it on my home wiki (enwiki) and others. Major kudos!
I noticed that ULS currently has button styles that very closely match the standard used in mediawiki.ui. Both seem to be based on the "Agora" guidelines from Pau and the design team, so it would probably save you from having to use custom styles if you convert to using the mediawiki.ui library.
We're already standardizing on it in Echo, GuidedTour, GettingStarted, as well as login and account creation in core, so if you need support or have feedback on how reusable the styles are, others folks in features engineering are available to advise.
I noted only converting the controls (i.e. buttons) in this enhancement request, because while the current version of mediawiki.ui specifies a font family stack, we're eventually going to phase that out in favor of applying any new font stack to skins, where they properly belong.