Your video has the 3D and 4K tags when I searched it. And does have the option for anaglyph and 2D.
I looked at other videos and those are the only two that are displayed (I checked using Chrome as well, not just Edge). I don't see "side by side"
Export/save in Autocad to the X3d format, upload that to your site, and use a VRML plugin for any of those listed players to view the file. Which means providing a link on the page for others to download the plugin so they can do the same thing.
I had the same problem with an illustration wich I would like to share using 3D effects. So, I discovered that 3D images on Facebook must have aspect ratio 2:3 or below, or conversion will fail. I changed my images aspect ratio (no other changes) and it worked perfectly! Try to do that too!