Hi, I wanted to comment on this as I used to have the same issue with my sync box and latest Apple TV.
I figured out a solution that works for me but still have a couple things that don't work.
First, I purchased high quality HDMI cables that do 8K 60hz and 4K 120hz. I ran it from the sync box out to the tv, and from my apple TV to my sync box. I use port 2 or 4 as they work better with the dolby vision setting.
Next I set the settings in the hue app to always start syncing when the apple tv is working. I also enabled ARC bypass.
As odd as it seems, there are times when the lights just stop syncing randomly (after many hours of use) and I use an ice pack in a towel, and put it under the sync box. Yes it sounds strange but I swear after a few minutes the lights start syncing again. I don't touch any settings or tap the sync button when the lights stop syncing, I just use the ice pack.
Another thing I realized is that the "interference" that I saw referenced everywhere was Homekit. We would use homekit (the home app) in the beginning to play with the lights but always had the issues of no sync. I guess there's a communication problem between the sync box and homekit. So we never use the lights with the home app anymore. it's still there as a light to click in the home app, but we never touch it. We still use and play with the lights in the hue app, never an issue there.
One issue I still haven't figured out the solution to yet is multiple sources. Sometimes it works where I'm syncing my apple tv and then switch to the playstation 5, and there are no problems. Other times it stops syncing. The sync function is still on but the lights don't sync. After about half an hour they'll randomly start syncing to my games but it is very random. So for now I only use the apple tv with the sync box.
So that's what I've done to get it to work and so far with just the apple tv, there've been no issues. No settings have been changed on the apple TV, I use the 4K SDR setting as it looks best on my tv.
Let me know if you have any other questions I'll do what I can to help.