In reality... there's probably no exact right answer! It's a case of going with your gut and figuring out what works.
Our dog was 8 months old when we adopted him. Cats have been with us forever. Neither had lived with the other species before.
We went real slow. Lots of boundaries (house line on dog at all times, x-pens used as room dividers, dog in pen overnight). Loads of training (especially on "stay" and "look at me"). Then a few months in, we let them just be more integrated.
It's now been 10 months and they coexist pretty well. Not perfect, but the cats are happy as long as doggo doesn't pester them. They have no problem sleeping in the same room. Dog wants to be friends with male cat and will offer him toys. Male cat just ignores him :D Female cat has swiped dog a few times, so he's nervous of her, haha.
We've always let the cats have more options than the dog. They can go anywhere they like. Doggo is the one who is restricted.
Kitchen is gated off (cat food + litter there).
Bedroom gated off (cats have the option to retreat).
Another thing we still do is put doggo in his pen to sleep for a few hours in the evening before bed. This gives the cats some dog-free cuddle time in the lounge, which they love. Could you do something like this?
If it was me, I'd find a way to let the cats rule the entire house again. I'd probably move their things downstairs, out of the dog's reach. Restrict your dog using gates, a house line that you hold or tether to something solid, an x-pen, etc. Teach a really solid "stay" and "look at me" before you remove those restrictions. Keep things positive, upbeat and light.
I'd think in my head: cats are the royals, dog is the peasant ;)