Can users see which permissions they have?

That was my understanding. Maybe something has changed?

eg. I am not a member of the “theme author” group. When I go to the category I see a “+ new topic” button that does not function.
theme - Discourse Meta

I know why because I have read
About the theme category

If you have developed a theme you would like to share, PM @sam and ask to be allowed to be added to the @theme_authors group so you can post your theme.

I don’t have much faith that members actually read what’s important to read, so IMHO it would be better to not show a non-functioning button. Better yet might be to have the button and show some kind of “you need to ask to join” modal.