@Crashillo looks like I can't click on the links on the tooltip, it disappears. Users should be able to interact with them, as per #4346 (comment) (see thumbs up by @decidim/product)

You can. First, you should click the author name, that action makes the tooltip to keep visible. Then, you're able to interact with the inner content.
The thing here is: Should we disable rendering the minicard on hover action? (just leave on click action) It's just a property, so technically is straightforward.
IMHO, I'd disable hover action, because is causing the missunderstanding you had.

@decidim/product can you chime in here please? ^

+1, let's proceed with @Crashillo's suggestion.

I've just included a hook to keep the tooltip open while the cursor is over the tooltip content

@Crashillo looking good! For what I understand, this design applies for both users and user groups, and when the author is an organization we don't show any tooltip, right? /cc @furilo