Morning JB, hope all is well. I may not be in the program but I sure can provide some clarity into this, as I am an IT engineer. Due to the way Steam works, basically it will only allow one install of a game on a device at a time. I suppose one way you could get round it is using a drive (or partiton on a rather big drive) with a dedicated Windows install for TSW or potentially a Virtual Machine (this would comprimise your performance though, so not recommended). There are ways to do it but it either is gonna be comprising your performance or your bank account. Hope all this makes sense.
Wouldn't you be able to move one installation of TSW to another folder? I have two working installs of Train Simulator on my computer and have had more in the past.
Steam supports different folders to install into. But the beta is not a separate game in Steam. It uses the beta feature of Steam which replaces the downloaded version of the game. If you have disk space to spare, you might try to close Steam, copy over the contents to another place, then start Steam and enter the beta code. It will then download the new files and replace your files in the installation location. If at some point you want to switch back, then you maybe can succeed by closing Steam, moving the beta content elsewhere, moving your old content back, cutting internet for Steam, start Steam and leave beta, verify files and restore internet. But this is incredibly hacky and will likely not work. Another option: you keep TSW 5 installed to game your old content and use the TSW 6 then for beta testing. Obviously, you wouldn't be able to play all the new stuff/experience the new features for your play sessions but if you just want to play a bit, that might be the easiest solution.
Backups and restoring the "stable" version will work. I'm not sure if Steam allows backing up of beta versions of games as I am not in any beta programs. What I have done with modded games is having two installations and naming the folders. Example, two directories "Red Dead Redemption 2-modded" and "Red Dead Redemption 2". When I wan't to play normal version I name it as it should be. When I want to play modded, I exit Steam and add "-stable" to the RDR2 folder and remove "-modded" from the other directory. Relaunch Steam and it will launch as per normal. This might work with TSW.