Hi!
The sound goes from the TV via the optical output to the soundbar. This means that if the projector has an optical output, it should actually work.

I would rather ask myself whether it really has to be Sonos. I regret every day that I chose Sonos back then, as these things aren't even worth the plastic they're built with. If they hadn't cost me hundreds of francs back then, they would have ended up in the hazardous waste bin a long time ago. Far too expensive for what they are, the app is a pure disaster and the sound is barely as good as wine UE Boom, which has fallen on the floor several times.
The low tones roll over far too early, which is why you actually need a subwoofer. Add that in and you'll feel sick.
Maybe I'm also "fussy" about sound quality, but I'm just used to music and not the sound of a pile of broken glass.
I hope I can prevent at least one user from making the same expensive mistake I did...