if you like the collecting aspect,
chicken smoothie is one of the best pet collecting pet sims. it's been around since 2008 and has a lot of different species and rarities you can collect and trade for.
if you want more gameplay-oriented petsims,
lioden and its sister site
wolvden both revolve around breeding lions/wolves with the specific genetics you want. you have to interact with and feed your pride/pack every so often or else they leave and eventually once they reach 15 in-game years, they die. they both have really cool monthly events!
pixel cat's end is a good in-between. you can collect cats and have them interact with each other every day and have them do different jobs to collect materials. there's an adventuring feature which mimics tabletop roleplaying games, which is very fun to me
there's no real stakes and your cats never die.
chicken.pet is still in beta (started in July of this year), but open beta launches on the 15th of this month! i don't know much about it yet since i'm not in the beta, but from what i can see it looks like a cute little project similar to flight rising but you collect chickens!