The Arc needs to go through the TV Setup process in the Sonos app while connected to a display that supports CEC before it will work with the Arcana and your projector. If you don’t have a TV with CEC, you may have to take the Arc to a friend or family member’s house to perform the TV Setup process for the Arc.
From the Arcana manual:
I cannot get any sound to a brand new/never used SONOS Arc from any source at Arcana input when Arcana is connected to a non CEC capable projector/monitor or display
In order to get audio from any sources at Arcana input, users of brand new/never used SONOS Arc must go through the APP setup process while connected to a CEC capable display. If you never went through the SONOS APP setup process with your SONOS Arc soundbar yet, please connect it to any HDMI display that offer CEC support and complete the SONOS APP setup process. Once done you can connect it back in your setup with a non CEC capable display, monitor or TV and you will be able to get Full Audio from any source to SONOS Arc as expected. This SONOS restriction requires such initial setup first with CEC capable display. If your SONOS Arc has been setup before, then there is no need to set it up again after Arcana is connected and you can just proceed normally.