I have a pair of X-T30-II's as they are light and dependable. I mainly use fixed focal length lenses, the more compact Fujifilm ones. However, for longer reach I have been using the 100-400 Fujifilm zoom. Yes, it is not the lightest but it is quite well made and works well for me, even though I don't like zooms very much. I picked mine up from a reputable e-bay seller,, and it works fine. The lens stabilization works well even though the body doesn't have IBIS. I'm not entirely sure what the "Pro" designation on some of the lenses Fujifilm makes as plenty of my compact fixed focal lengths don't have it on them and they are superb pieces of glass. Frankly, if it works for you I'd just ignore the "marketing" labels.
Now 400 mm doesn't seem like it has that much reach, but remember this will be the equivalent of 600 mm for a full frame digital or 35 mm film camera. 10 years ago, unless you were a professional photographer hiring obscenely expensive lenses, 600 mm was a very long lens for anyone to own. That is a lot of reach. Anything more than that is going to be substantially larger, probably heavier and with less light transmission, oh and very much more expensive.
I like the 100-400 mm a lot, especially for the money, and it gives me very reasonable results. I'd take mine with me on a safari any day. I think you will be able to keep far enough away from the big kitties to stay safe. I use mine with a mono-pod quite often, and with the lens stabilization is turned off.