I think I’d collect information about the owner in custom user fields. Then those are attached to their profile, and if you add them to the user card, they are only one click away on any topic.
Maybe the cats fit into topics - one topic for each cat. Then users can link to that topic in their other posts.
The portfolio component comes to my mind, too. Maybe the category for the cats could be a portfolio category. The portfolio is linked on the usercard as well.
Something like this:
But the portfolio only works for your own posts. So that’s not the perfect solution for 2 people caring for the same cat(s). Maybe one of them could add the cat’s topic as their featured topic (that would work only for one cat) or add a link to the other owner’s cat portfolio in a link field of the profile (maybe in the website field? You could change the text so it no longer says website). There are also theme components which add links to profiles: Custom Profile Link & Multiple Custom Profile Links
That are some components that come to my mind.