From what I've been reading, the only substantial change Apple made with the release of iPadOS 16 that impacted the use of iPads with HomeKit, was that iPads can no longer be used as hubs, in favor of hubs that are always plugged in, like the Apple TV and HomePods. Apparently Apple feels that hubs should always have access to stable power, and not just battery power. But from what I'm reading, the Home app on iPadOS 16 and up, and the iPhone's iOS 16 and up, are identical as far as their ability to still function as controllers for these hubs. So both iPads and iPhones, by themselves, since they can't be hubs, can no longer manage HomeKit background tasks, automation management, remote access, or Matter device compatibility in the same way as dedicated hub devices like Apple TV and HomePod, and instead you use your iPad or iPhone as just the controller to tell the hub how to perform these tasks.
This doesn't address whether the Home app on iPads and iPhones will be usable as controllers for this supposed new hub as well, so that you don't have to always use the new hub's little built-in display to control it, but I guess I'd be a little surprised if Apple blocked support for using iPads and iPhones as controllers for it. But I can see the reason for having an always-attached display (even a relatively small one) for use as the hub's main controller, rather than requiring an iPad or iPhone which someone in the household might walk off with and use elsewhere.