I am running iOS 15.2.1 (the latest) on both my iPhone and iPad and macOS Monterey 12.1 on my Mac.
I need to make a correction to my original post. "Home" can only be found in Settings on the iPad (just under Shortcuts) - the iPhone and Mac do not have this in Settings. The Home app, with the configured accessories, is on the iPad, iPhone & Mac. (I was rapidly going back and forth between all devices comparing everything I could regarding the Home app between them. I accidentally grouped the iPhone with the iPad when posting.)
I had only posted the confusing text from Settings-->Home in the previous post. Here's everything else in that setting:
- "Use this iPad as a Home Hub" with a toggle on/off.
- "Using an Apple TV (4th gen or later), HomePad or an iPad as a home hub allows automation, remote access of your accessories, and provides more powerful user permissions. iPad must remain in the home and be continually powered on for these features to work. Learn more...
- "You currently do not have any homes or invitations to homes. Create homes in a HomeKit supported app."
Note - toggling on/off (& waiting days in between to see if anything updates) does not seem to change anything that I could see.