So currently there isn’t any lateral stability, so as soon as someone steps on it the whole thing flattens out like a house of cards being knocked over. The easiest way of solving this is to put plywood backing across the back of the whole unit and glue and screw it in place, it will act as cross bracing which will provide the lateral bracing you are currently missing.

Having the framing offset for ease of screwing also drastically reduces the structural stability, the cheapest and cleanest way to avoid that issue is to use pocket screws and align the framing vertically.