Hi. You cannot connect the Beam to an HDMI port on the projector, unless it has HDMI
-ARC, which is rate on a projector.
There are lots of threads on here discussing projectors and Sonos so I think you should have a bit of a look through some of those.
Projector has 2 hdmi inputs
But no HDMI ARC output? That is what the Sonos is looking for.
Unless the projector sports an ARC port, use an HDMI audio extractor of some flavour.
Either one which outputs optical, used in conjunction with the Sonos optical/HDMI adapter. Those often come with in-built HDMI input switching.
Or the HDFury Arcana which generates HDMI-eARC, and connects to the Beam directly.
Thanks very much. Sounds like that is the solution