Best way to integrate Hue Lamps, Hue bridge and Hue Sync box

Hello together.
I am completely new to home assistant. I set up my HA green yesterday and did the first steps.

Since I am a huge fan of the Philips Hue Sync box, I am wondering what the best way is to integrate it.
My research resulted in the fact, that the Sync box needs the hue bridge in order to work.

Does anyone of you know if my hue bulbs that I want to use with the sync function also need to be connected to the Hue bridge, or can those can be connected to Z2MQTT?
Or do I need to have one Group of Lamps running on the brigde together with the sync box and another group for all other hue lights running on Z2MQTT?

Thanks in Advance!