I checked again to be sure. What I listed above are the named options on an iPhone 14 Pro under iOS 16.5.1.
But on my 6th gen iPad (also iOS 16.5.1), the choices are quite different. I made the mistake of assuming they'd be the same since it's the same level of iOS.
Anyway, for the iPad, iMessage is on. The phone number/address for send and receive are the same. Beyond that, Shared with You, Send Read Receipts, Show Subject Field and Notify Me are on. The other options on the iPhone don't exist on the iPad.
Despite the drastically different option choices, they do sync.
And that may be directly related to how Apple releases their OS's. Almost every time there's an update or upgrade to iOS, there's a macOS update/upgrade. Meaning, it may be important to always have the latest OS installed on each device. But I'm once again guessing on that.