Only downside is that I will likely loose Dolby Atmos sound since this think probably doesn't support it.

Close. But I was suggesting that you use a matrix switcher, not an audio extractor. A matrix switcher has 1 (or more) HDMI inputs and 1 (or more) HDMI outputs. So, for the sake of example, let's say you get a 2x2 matrix (2 in 2 out). You plug your PS5 into one of the inputs, leaving the second one for future use like an Apple TV or something. Then run one HDMI out to the projector and one HDMI out to the Beam and configure the matrix to simultaneously send to both outputs (matrixes are configurable with little toggle switches to set different settings/resolutions). As long as the matrix is doing full pass-thru of audio, Atmos should come along for the ride.

The only reason I mentioned an optical out was as a backup. Most HDMI matrix boxes come with an audio output already. I mentioned it only in the case that for some heretofore unknown reason the all-HDMI solution doesn't work. But I really think it will work. But the other person is correct: no Atmos over optical.

Just remember as I said to pay attention to the resolution/refresh rates and to not get one that will limit you down to 1080p/30hz, for example. In the price range you are asking, you can find a matrix that can simultaneously output 4k@60hz for sure. If you need dual 4k@120hz, you're looking at the next price range of 100-200 dollars.

Here is one I quickly found as an example. Couldn't find any 1x2 or 2x2, but here's a 4x2: HDMI Matrix Switch 4x2 Switcher Splitter 4 in 2 Out