Introducing a new puppy to existing cats

[SoFuckingTired]

Has anyone done this successfully and can give any tips? Hopefully getting a new pup early next month so trying to be prepared. We have 2 cats who are confined to the kitchen/utility overnight but spend most of their days upstairs. Plan is to keep them apart at least initially, so pup will sleep upstairs and swap during the day. Naively thought it would be fairly straightforward but the more I read the more worried I become!

So we banned the puppy from the upstairs as then the cat had somewhere to escape to.
The dog is crated overnight in the kitchen. Cat comes and goes through her cat flap.
the cat is not a massive dog fan, but she tolerates him now, there were quite a few hisses/growls and swipes when the puppy was tiny.

Basically, you don't introduce them. You make sure there are places the cats go the puppy can't, that the cats always have a clear exit to their cat flap (so wherever it is the puppy mustn't be able to be waiting for them or chase them to it). Never let the puppy chase or 'play' with the cats.
Using baby gates or dogg-8 (really useful items as they can go across big spaces and are flexible to let the cats look at the dog if they choose is helpful

Stage gates so that they can see each other it leaves the meeting up to the cats and the cats will have their own safe space they will mix when they are ready

Let the cats tell the puppy off they need to make sure it won't hurt them when it's bigger

Mine are best buds now but it took a couple of months

Stair not stage sorry

We made upstairs the cats area, food and litter tray upstairs, dog downstairs. Dog was crated overnight (I slept downstairs with him for the first few nights). As the cats got braver they would sit on the stairs and watch. Sometimes in the day we would crate the dog so the cats could come downstairs etc. Took a couple of weeks until the cats took to him. They are best of friends now!

Thank you, so basically no introductions, keep them separate and leave it up to the cats when they interact?