I went to the trouble this weekend of doing a factory reset of my Hue Hub, re-adding all lights/rooms, only to be right back at square one with the same issue of all my Hue lights displaying "No Response" in the Home app. I even went one further, as I had a spare, and slightly newer, Hue Hub lying around that I got from a starter pack a while back. I nuked the newly reconfigured hub with a factory reset and removed it from my Hue app. Then, I went through the process of setting up the newer hub with all the lights/rooms again and had the exact same problem - status of all Hue lights as "No Response" in the Home app.
What's odd is that I can still control all the lights through the Home app just fine, and if I click into 3-4 lights, then usually all the lights in the Home app regain their proper status and display correctly (if they are on/off and their current brightness level). In the Hue app and also in the Controller for HomeKit app (a third party app not by Apple) the lights always display the proper status of all my Hue lights. It seems to be just the Home app by Apple is the one behaving in this manner.
Just a little bit of additional info; I am running the latest iOS 16.5 on my iPhone, my HomeKit hub is an Apple TV 4K that is hardwired into a gigabit ethernet connection, which is also running the latest tvOS 16.5, and I have updated to the latest HomeKit architecture.