As long as that projector has ARC or eARC, your Sonos Arc should work well. 

The PS4 Pro doesn’t support Dolby Atmos audio on any streaming services. It only supports Dolby Atmos audio from Blu-ray discs AND only if your projector is equipped with HDMI eARC or you are using an HDFury Arcana eARC adapter.

Thanks for the quick reply! I actually have it now connected to a standard 5.1 system and it decodes dolby digital so I assumed it could do dolby atmos if connecting this soundbar.

so how about a chromecast 4k? Would it work?  It would be connected the same way ( chromecast to projector and then to sonos arc)

Or this can only be achieved with smart tv app+sonos arc?

The PS4 doesn’t support Atmos audio from any streaming service regardless of the soundbar you are using. The PS5 is the same.

The Chromecast with Google TV (2020 model) supports Dolby Atmos only from Netflix and Prime Video. But you need to check if the projector can pass through Dolby Atmos audio.

Your best option would be to get the Arcana eARC adapter and get an Apple TV 4K or Nvidia Shield. Both devices support Dolby Atmos on Netflix, Prime Video, Disney+, Apple TV+, HBO Max, and VUDU.

Thanks again. It seems most likely one has to spend 500 extra dollar with those two devices. Thanks Sony. 
 

I wonder why Sonos didn’t just add another hdmi to input directly from the source and then not having to be guessing whether the device can pass through audio codecs, limiting the Truehd audio, etc. just like any other soundbar does.

if I buy the pair of sonos one, the issue still remains the same, or it is automatically converted to dolby digital 5.1? And that’s better or worse than atmos? I was actually thinking of buying them. 

Yes, the issue will remain the same. You will still not be able to get Dolby Atmos from the PS4. But adding a pair of Sonos Ones as surrounds to the Arc will definitely give you a more immersive surround sound experience even with just Dolby Digital.

Dolby Atmos audio usually sounds better than standard Dolby Digital, but oftentimes Dolby Digital audio is sufficient.