I have updated 4 HomePods, 2 HomePod Minis, 3 AppleTVs, an iPhone 14 Pro, a first gen iPad Pro, 2 MacBook Pros to all the latest OSs and everything is working fine. Automations are working and I can control all my devices from any of the devices that allow it. Everything was working fine before the updates and everything is still working fine. I set all the HomePods into updating from the Home App on my iPhone last night and did each TV on screen in the AppleTV Settings.
1 AppleTV is set as my Hub and all the HomePods are in Standby. The AppleTV that is my Hub is also on ethernet not WIFI (better speed that way) and who knows if this has any effect but want to give out as much info as I can.
I have 18 devices that always come up as "No Response" (they are Insteon switches and plugs) but when I click the settings dot on the Home App home page on my iPhone and start clicking on each of the "No Response" devices after I click on about 5 of them they all respond. Works different with less success if I just click on the left side of each device button on the home page itself. All the rest of my attached devices (Wemo Thread plugs, iComfort Lennox Thermostat and Eve Aqura) show up just as they should every time. The Insteon devices respond to automations even when they show "No Response" so it's not a big deal.