I don't know if "favorite" accurately describes my relationship with Rare's
Viva Pinata but it's a pet sim that's stuck with me and I think it's primarily due to Rare's injection of their on-brand absurdity and straight-up trolling
I only ever played this game as a adult and I found myself wondering, on multiple occasions, if this game was the culmination of Rare's contempt for children, who this was clearly marketed to. When I say this game trolls you,
I mean it.
That aside, the only truly retro pet sim I can think of off the top is
Jade Cocoon (1998) for the Playstation. It's a short-ish RPG where you raise mostly bug monsters but the breeding and merging mechanics are fairly complex.
Also, Katsuya Kondō, the character designer for
Kiki's Delivery Service, helped develop it.