I am a similar issue. Have a number of automations running just fine on HomeKit (Apple TV HD as the Hub), but this weekend, I tried to add a new automation and noticed that it won't work. It seems like while all my existing automations are working, no new automations would trigger. I can set it up, it works when I test it in the automation UX , but it never actually triggers in real use. I tried some really simple ones like when this light turns on, turn that light on too, and it still doesn't work. Note that I can see and control all my accessories, old automation work, but new ones don't. I am hesitant to make changes to my old ones in case they break too, I spent too much time setting them up.
My Apple TV is on TVOS 16.1 (must have recently auto updated), my phone was on 15 something, and I just updated it to 16.1.1 but the problem is still the same.
Any one have the same issue (old automations work, but new ones doesn't) or a solution?