This is a HUGE wisteria in the Japanese Collection at the National Arboretum. It features a "weathered" trunk that, at one time, rotted away significantly. It has since regrown over most of that damage. I would suspect the original damage came from it's collection, or from damaged wood while in the ground. At any rate, this kind of thing can be worked into the final design of the tree. With yours, it looks like you've still got some pretty decent growth from one side of the trunk. I'd just let that go for a few years and get established and put on more wood to compensate what you've already lost and what you will lose on the other side.
Use wood hardener if you like, but lime sulphur will probably be a better choice for its antibacterial and antifungal properties. With wood hardener you get none of that and FWIW, water will soak into the wood BEHIND the hardener and rot from the inside, leaving a shell of treated wood that will collapse in time--had this happen with a huge wild rose vine I had a while back, and that plant produced denser wood than wisteria...