It only truly works, in my experience, if the adult cats were there first, and then a sighthound puppy is introduced secondly.
It's important that the cat/s are allowed to firmly put the puppy in it's place early on, so that it grows up being wary of them. My hound will still have a half-hearted chase if the cats are chasing each other particularly energetically in the house. She is scared of them, but she still does chase occasionally and I am very aware that nothing is certain, one day she might flip and kill one of them. Mostly they just warily coexist. I don't let the cats near when she's eating or sleeping.
It's innately wired in them to chase. My own was raised in the manner described above to live with our cats but spends her every opportunity plotting to kill the neighbour's cats. And I am certain she would kill those ones if she got the chance. When she is in chase mode, she would run through a barbed wire fence and barely notice... She's injured herself tripping in holes during "chase mode", and that was just chasing me.. It's like a switch goes off and they lose their brain, and become a single-minded speeding idiot lol. You wouldn't stop them if they decided to kill a cat, they'd be too quick.
However, she's come face to face with a massive cat on a walk, and I didn't have time to tighten her lead because he was hiding behind a car. My dog instantly went to attack him, I snatched at her, but the cat just stood his ground and she immediately backed off. It was a big shock to me. She's a whippet though, if she were a greyhound that cat would probably have been hurt or killed.
I've had farmers ask to use her for rabbiting and I refused because I don't want her getting a "taste" for it, even though that's what she's literally bred to do lol. Best not tempt fate!