Looking inside that theme component gave me a bit of the answer I was looking for — mainly that muting a category won’t surface it to people who haven’t created topics in that category. So it doesn’t appear for people.
Trying to work with user groups though notably doesn’t work — the category being set as non-visible for anyone besides admins means that the topics themselves are also invisible. I surface some of the “CMS” stuff as pages on the site so those do need to be visible when accessed.