Sonos Arc needs an ARC connection. Your Samsung likely has ARC built in, but it’s unlikely that your projector does. And the ARC on the Onkyo is likely a pass through, and wouldn’t have the ability to create the ARC signal like your TV probably does. 
 

Most people who want to use a projector end up with either an HDFury Arcana, or the equivalent type of device from a company I recall as Feintech. Both of these devices are able to create an eARC signal from a normal HDMI input, and feed up to Atmos to the Sonos Arc. There are quite a few threads about this. 

Trying to wrap my head around arc vs earc etc so apologies in advance if I get any terms wrong!

For an hdmi switch to work passing dolby atmos signal to the arc, I'm trying to work out what switches actually work.. 

I have and arc, a (standard noe arc/earc) hdmi switch with inputs from sky q box (some atmos support), a 4k chrome cast, and xbox series s. With hdmi out to an optima projector (no arc/earc) and optical out to optical dongle included with sonos arc.

Net net is I get 5:1

But wondering what I'd need to add dolby atmos. 

So, 

From what I can gather, adding the hdfury arcana between the switch and projector should work? Or is that then dependent on the specifics of the switch? 

Or, would this work (it says arc, and, looks like has an arc supporting output port) https://www.amazon.co.uk/gp/aw/d/B01LXAJ5YI?psc=1&ref=ppx_pop_mob_b_asin_title

But seems a lot cheaper (yay) than others so is it too good to be true?

So, what is they key protocols I need to look for?

Hope above makes sense. And again, apologies if I've missed (or more likely, read and not understood) details elsewhere on the forum... 

The differences, at least for your mind, between ARC and eARC should likely be just bandwidth. One carries a lot more bandwidth than the other, but from the user perspective, they work essentially the same.

In order to add Dolby Atmos to your system, you would need to add either that HD Fury Arcana, or the Feintech devices. They would go in between your source devices, and the projector. The Arcana has a single input, so you could put a normal HDMI switch in front of that, if desired. I’m not as familiar with the Feintech, but I think they either have four HDMI ports built in, or have another device that does...check on their website. 

The switch you linked says this:

• 【ARC Function】--This switch supports ARC (Audio Return Channel), Extractor the audio from TV to Soundbar or Amplifier. Connect your TV HDMI(ARC) Port to this switch HDMI "OUT A" port with HDMI cable, then connect an optical cable to the soundbar, Speaker, home theater, A/V receivers, etc. Only the "OUT A" port supports the ARC function. Support Dolby Digital (AC3), DTS and LPCM2.0 audio format

This means that they’re relying on your output device (the projector) to provide the ARC data. Which you’ve said yours does not do. And then they send it to an optical output, which doesn’t have the bandwidth necessary to carry an Atmos Signal, so you’d only still be getting Dolby Digital. This is why you need the HD Fury Arcana or Feintech device, they have the electronics inside them to create that eARC signal, and send that to the Sonos Arc. 

Somewhere around here (and I’m looking at you, @Ken_Griffiths ) some kind folks have posted links to both the HD Fury and Feintech sites. I’ve unfortunately not saved them myself, since I already have an HD Fury Arcana, and the Feintech is challenging to get here in the states. If you did a google search (not the forum search, the results from that are random), you’d likely find that reference. Or perhaps Ken has that handy, he’s a good person :)

@bakesteve,
Ideally you need HDMI-eARC to get Atmos and any form of multichannel PCM uncompressed audio although technically, compressed Atmos DD+ (Atmos) is available on some products that have ARC only, but it’s more rare than the norm to see devices with ARC only supporting Atmos.

The image summary (attached) shows the differences and the available bandwidth supported by ARC/eARC ports.

To bypass a TV, or device, that doesn’t support the Atmos codec, many people use a device like an HDFury Arcana and a 4K capable switch (normally supplied with its own power supply) - the setup with a Projector looks something like this:

There are other devices on the market that work as a combined switch and audio splitter too. Two others I’ve seen mentioned in the community here are:

Feintech VAX04101A

https://feintech.eu/en/collections/hdmi-topseller/products/feintech-vax04101-hdmi-earc-pass-switch-4x1-for-soundbar

Or…

OREI HDA-931

https://www.orei.com/products/dual-hdmi-earc-audio-extractor-converter-4k-60hz-18g-hdmi-2-0-arc-support-hda-931

Here’s the HDFury Arcana link too:

https://www.hdfury.uk/product/hdfury-arcana/

I knew you’d have it handy :)