how do I separate the iPhone from my iMac and laptop?

On your Mac to keep iMessages off go to the app and sign out. You will still get them on your iPhone.

You’ll usually need to create and use a different Apple ID, as Apple IDs are assumed to be the same person.

It’s probably possible to restrict to just SMS, and avoid using iMessage which’ll send across associated clients, and avoid referencing that telephone number elsewhere, not that I’ve tried that.

Well, I've never used iCloud services, nor have I synced anything on one iPhone, two iPad Pro's, one MBA, and one iMac. I've been doing this for a few years with varying devices.

They are definitely separate entities; if I take a pic on my iPhone, I have to use Airdrop to get it to any of my other devices, so none of them talk to each other. If I create a document on my iMac, I have to airdrop it or copy to an external SSD which I then plug into the other device. My iCloud space available is 5 GB. It is not as "convenient", but this is how I want it. You do need to disable/undo several automatic settings when setting up a new device or new install since Apple wants you to use it. So I do - takes a couple of minutes to check all System Preferences Panes. As an example: I do not want Game Center; I have never opened or activated it; I would rather delete it, BUT: Apple thinks I should use it, so every time I set up a new device or have a reinstall, Game Center is automatically checked/activated. Quite annoying. The same with Notifications: most are on. I painstakingly disable them all every time.

Sorry, rather a long explanation here. The gist of it: it works.

I use the same Apple ID for all devices, BUT: I do not have iCloud or syncing enabled. None of my devices "talk" to each other - they are all separate.

So, unless you need it, simply turn off iCloud syncing on all devices and see if that works.

Same Apple ID means same user, so I wouldn’t depend on that not-using-iCloud-separation here. Try it, but...