I just upgraded to an iPhone 15 from a backup and figured out that the login to iCloud associated with the Apple Watch did not transition, and while the vast majority of features and functions of the watch were transferred and operational through the Bluetooth connection HomeKit accessories is one area that does require the iCloud account. Once I figured out that the watch was not logged into iCloud it solved my issues. This is what I did, mind you steps 1-3 may not be necessary, I was trying all sorts of things to figure it out.
1 - On the watch turned off WiFi and Bluetooth.
2 - Rebooted the watch.
3 - Turned the watch Bluetooth on.
4 - On the iPhone and in the Apple Watch select General then Apple ID
5 - Enter the Apple ID Password
Once completed I saw the HomeKit app on the iPhone populate with all of my accessories, scenes and favorites.