If the exe runs by itself, then the Oculus SDK should be working. If you get some sort of error message when launching from Steam, that sounds to me like a Steam issue. Where does it look like the error message is coming from?
On my opinion it seems like something related with the Steam Launcher or whatever wrap they make to executables. I have configured everything on their end, paths, frameworks, that it should use on launch (Oculus), etc., no dice. I also have no error logs on Unity as well. This is really baffling 😞