We bought the van, and there are things I would have done a little differently, but this is the setup.
Full sized mattress, and some "cabinets" on the passengers side for storage.
The bed platform is literally a 1/2" ply platform with 1/2" ply for support, with 1"x1"s at the bottoms and tops of the supports to help anchor to them. This is Essentually the back done of the platform. There are 1"x1" supports on the ends as well that support a horizontal plywood stringer across the van (which is screwed into the body as well). At the front/back there is a 2x4 mounted to that stringer.
Clearly the guy that built it was a wood worker / dooms day prepper, because its WAY overkill and the space below the bed is really oddly shaped which makes it hard to use.
If I had to build a platform bed I'd use E-track mounted to the body (or stringers if you are finishing the inside) and make it a little more adjustable and ditch most of the support. I ran E-track up to 8' spans with 2x4's in a few trailers for tire racks, bed frames, etc and loved it. 1/2" ply and a few 2x4's will hold a TON of weight.
Hope this helps!