I bought these ages ago for different reasons and am hoping they will work together, but I think the Shanny is a bit "Dumber" I've searched and searched, so now I'll show my ignorance and just ask. Anyone know?
The YN-E3-RT clones the Canon RT system and should be compatible with other devices that use the Canon RT protocol. There are a lot of reports from users that when trying to use two third party devices from different makers that both clone the RT system there can be issues with the two third party devices working together. The only real way to know for sure in that situation is to try it and see what happens.
The Shanny SN600EX-RF is not a Canon RT clone, though. It uses Shanny's own proprietary RF (radio frequency) protocol.
The only way to trigger the Shanny SN600EX-RF with Canon RT components is to use the Shanny in "dumb" optical slave mode and trigger it with the light from another flash. S1 slave mode is for use when the triggering flash is in manual mode and only fires once when the image is being exposed. S2 mode if for use when the triggering flash is in TTL mode and fires a fast series of pre-flashes before the exposure. The "dumb" slave flash set to S2 will hopefully ignore the pre-flash and fire when it detects the main flash pulse.I use "hopefully" because S2 mode can be a bit hit or miss, particularly if one is also using red-eye reduction and TTL which each have their own series of pre-flashes.
To use the YN-E3-RT on your camera to trigger the Shanny SN600EX-RF, you'd need another remote flash that is Canon RT compatible. You would control the RT flash with the YN-E3-RT and the flash burst from the RT flash would trigger the SHanny in "dumb" slave mode.
Or you could use any flash directly on the camera's hot shoe if the camera can trigger a non-Canon manual flash with a standard ISO compliant hot foot. Please be aware that a few of Canon's cheapest cameras, such as the Rebel T7/2000D and Rebel SL3/250D among a handful of others, no longer have ISO compliant hot shoes with a standard manual flash pin in the center of the hot shoe. For those cameras one would need to use a Canon TTL capable flash, even when desiring to use it in manual mode.
Another option would be to attach a Canon RT compatible receiver to the hot foot of the Shanny flash and set the flash like it is attached to a camera's hot shoe. The receiver attached to the flash will act like it is the camera as far as the flash is concerned. Your YN-E3-RT would communicate to the Rt receiver attached to the Shanny flash.