Help – I feel like I’ve made a massive mistake.

I've always wanted a dog, jut really craved that companionship you get with a dog. I'd personally always liked the idea of adopting an older dog, skip the puppy part, have no interest in children, so why go through the pain with a puppy.
However, we have two lovely cats, and after looking at an older dog recently and deciding against it for the cats, the shelter asked if we'd be interested in a puppy from a litter they had coming. A puppy, while hard work, would be overall easier with the cats, learning to live with them from a young age.
We got our puppy on Saturday, he's roughly 8 and a half weeks, so still super young, and I know it's extremely early, but also, WTF. The adjustment has been insane, people warn you, but my god, I was not prepared.
I think I could handle the general puppy chaos, but it's the cat side of things that's really making me anxious. We're generally pretty lucky, he naps in his crate, got a 90 minute nap from him today, and he sleeps in his crate overnight, only 2 wakes a night so far. Toilet training is going relatively well for a pup so young, so cannot complain. But we're having to keep him separate from our cats. We've got him in our room and set up a zone in the garden leading out of our room, then he has a puppy pen in our hallway, with a fence thing up into the main living area, so he can see the cats, but can't get to them. Today we had two cat interactions outside, and I cannot help just panicking. He has growled and barked, the interactions were with the little garden fence we put up between them, however both times each cat has managed to sneak into the fence area and give us a bit of a surprise.

Has anyone else successfully introduced a puppy into a house with cats? I need tips, or advice or reassurance, as right now I can't help but think, is this actually going to work? And if it's not, this was a horrible idea. The only reason I thought ok, about going through the puppy madness was for the possible cohabitation of the dog with the cats. I don't need friendship, just coexistence. I know it's super early, but I can't help spiraling.
Breed wise, he is a staffy x, likely with a whippet, but they're not 100%. He's very sweet, like for his age I cannot fault him, he's done nothing but behave like a puppy.