I have tried a few, seen below, but most either aren't what I was looking for or were costly to start/not worth starting. I'll still try to give a fair review just in case others may enjoy them tho.
What I'm looking for: (! = want; !!!! = need)
Realistic Genetics (I am familiar with cat genetics and want to expand my knowledge) !!!!
Showing/Standards !!
Rollovers/Locking !!!
Non-player bred starters/New cat generation !!
Realistic art !
What I've Tried:
Mweor
Super fun, still likely going to play it, but the genetics are just- not there. Though it's super easy and fast to start, money is easy to come by, and you can get a lot of desirable/cool-looking traits for pretty much free. I thought it was realistic when I tried it as it was recommended in FurryPaws, which is a very realistic game.
Edit: After playing for a while, the game ended up not being for me as it's much more stat breeding than genetic breeding. It got a bit repetitive for me, though people who love fantasy games could have lots of fun.
Cyska Siberians
Absolutely adorable art, and I love that you can play with a 3D render of your cat! Gentics are pretty much perfect! Only problem? It's entirely pay-to-play and expensive. You can get one free cat when you make an account, but other than that, you need irl money to get the primary currency so you can buy decent food, breed (yes, each breeding is locked behind a paywall..), get new cats, and pretty much everything else. I'm currently trying to see if dumping the $50 to afford one breeding is worth it. However, it is the most realistic out of the group. Time passes as normal, with cats living for literal years. I'd initially joined years ago when it was planned to be a FooPets revival, and my cat was still alive and cared for by the foster system so I wouldn't lose her. That being said, you still can definitely lose cats, and I've seen sad stories about people's cats running away only to be claimed by someone who couldn't care less about getting it back to them.
Edit: You can technically get cats for the "Free" currency, but the grind almost isn't worth it. You can rescue cats from the woods for 100,000 points, which would take literal months. You generate Points by logging in and getting the top 5 scores in various games. In one day, playing every game, I could only win ~1000 points, shown below. The sad part is that I also had to pay ~2000 points to feed my cats, more than negating the gain.
Another Edit: The game takes 100% real time, meaning I won't find out if I made any of the premium currency until January. The game has been rather fun for me, but it is definitely pay to win which is a bit frustrating.

Transcript:
November 8, 2024, 6:55 PM - Received prize for playing Dress Up Time at the Arcade (+) 10 PP
November 8, 2024, 6:53 PM - Received prize for playing Dress Up Time at the Arcade (+) 10 PP
November 8, 2024, 6:51 PM - Received prize for playing Tower Blocks at the Arcade (+) 40 PP
November 8, 2024, 6:49 PM - Received prize for playing Mancala at the Arcade (+) 10 PP
November 8, 2024, 6:44 PM - Received prize for playing Klondike Solitaire at the Arcade (+) 100 PP
November 8, 2024, 5:59 PM - Received prize for playing Klondike Solitaire at the Arcade (+) 100 PP
November 8, 2024, 4:31 PM - Received prize for playing Klondike Solitaire at the Arcade (+) 100 PP
November 8, 2024, 3:21 PM - Received prize for playing Marble Lines at the Arcade (+) 226 PP
November 8, 2024, 3:01 PM - Received prize for playing Bricks Breaking Hex at the Arcade (+) 34 PP
November 8, 2024, 1:30 PM - Received daily login points (+) 400 PP
Pure Felinity
Currently trying this game. It seems fun and it pretty realistic, but the breeds/standards system is a lot to wrap my head around. I might be breeding toward a specific breed, but who really knows aha- It takes a bit of digging to find cheaper cats that aren't neglected, but I've found that just searching all breeds instead of a specific one helps. The art is generated similarly to FurryPaws, and the personality system is a nice touch. The UI is a bit confusing and the ability to add player-made breeds is a little bit of a headache when trying to breed one breed, but as long as you've played games similar to this before you should be golden.
Edit: The game ended up being pretty fun. The only annoying part is that it doesn't display the genetics and you have to track them the old-fashioned way. It can be a bit of a hassle to breed out recessive genes, and the only way to figure out what genes are actually in the game is to reach through the Wiki, which isn't super clear either.
Pixel Cat's End
Super casual D&D but not-cats! It's not really a showing sim, but the genetics are pretty realistic! You essentially get to tell your own story, and it's super inclusive regarding gender, sexuality, and relationships! If you love D&D and have even a small interest in genetics, this game is great!
Edit: Playing for a while is pretty fun, though it really isn't a breeding game either. You can't control what cats get together and have beans (kittens) so there isn't a lot you can really 'breed' towards
Waiting to Try:
None at the moment!
Not Interested In:
PawBorough
I've seen some people mention this game in other threads, however this game doesn't look to have any sort of genetics (at least of the realistic kind). The art does look adorable but I'm not really in the market for Flight Rising but cat. Not to mention it's Closed Alpha so I can't exactly try it anyhow aha