I own a PS4 (non Pro) that sends HDR to my TV. It is connected to a normal (non ARC) HDMI port. Your assumption that a PS4 needs ARC for HDR is not supported by my set up. As I understand ARC (Audio Return Channel) it is all about sound, not colour.

I'm also not sure if the sync box might need ARC. In the reviews I have read it is not mentioned as a condition. Have you tried the HDMI Bypass optione mentioned here: https://www.homecinemamagazine.nl/2019/10/review-philips-hue-play-hdmi-sync-box-ambilight-2-0/, (sorry, text is in Dutch).

If the bypass option does not work, I would try connecting the Sync box to a normal HDMI port and the Beam to the HDMI ARC port on your TV. As I understand it all images will still pass through the Sync box  and the TV will pass the sound via ARCV to the Beam. Can you try that?

ACRV=ARC (typo)

Thank you @106rallye for your response! I was able to connect the Sync Box to a different HDMI port and the Sonos to the ARC port and it seems to work. I also was able to use the optical cable and connect the Sonos that way while leaving the Sync Box to the ARC port. 
 

Just a follow up question and sorry if I’d a dumb one, my knowledge about audio/video related topics is limited. Is there any downfall of using the optical input to connect the Sonos instead of the ARC HDMI port? Do I get degraded sound? Any latency issues during gaming?

Thanks!

When using optical instead of HDMI to connect the Beam you need to teach the Beam to be controlled by your TV’s remote For example.. HDMI takes care of such things. HDMI-ARC is the preferred and standard method of connecting the Beam to your TV. If that works in your situation I would prefer it above the optical connection. I do not think sound is degraded when using optical, but some TV’s do not pass through surround from HDMI to optical.

There is zero difference between Dolby Digital carried via HDMI-ARC or optical. 

Thank you @106rallye and @Airgetlam for your responses. I appreciate all the help!

Cheers!