I would think that if the transfer switch frame and the cabinet come together as a single unit, or if they are intended for each other, and are listed for use at the current levels involved, that they would have engineered it, and checked it for listing, for the appropriate wiring installed.
But it certainly looks to me like it is stuffed on the right side.
A closer look and I see the top feeds have 1 phase (brown) and what I assume is neutral in the leftmost conduit, and the other 2 phases (orange and yellow) in the 2nd conduit from left. What comes from or goes to the conduits on the right are not marked within the frame of the picture.
