Sure it is a good looking project, contemporary and clean. .....but
Image the weight loads moving through the structure when you look at such things. Even people who are not engineers can learn to do that kind of thinking when designing, building, or selecting van beds and cabinets. Also for how they are attached to keep them in place.
1st note: Ikea discontinued selling those particular shelf brackets.
But the bigger issue, this is a very poorly thought out design for a bed. It would work for occasional use for a lighter weight person, but not for an average or heavier weight person because there is no center support under the plywood or else a substantial support beam along the edges of the sheet goods. The plywood itself, even with the small doubled up strips along the edge will quickly sag. It is especially a problem for use in a van where the bed often doubles as a couch. So that means a persons full body weight is often centered along the front edge of the bed. It works best to put legs on the front and back edges right under person would most often be sitting to transfer the weight of their body directly down to the floor. Or divide the length of the space up and put two extra legs on both the front and back edges to distribute the load of the body weight of a person down to the floor while supporting the surface they are sitting on.
When you design platforms, cabinets, beds etc you always have to keep in mind how the loads are supported and do anyalytical thinking of how that load is distributed on down to the floor. If you don't have some type of a strong, load bearing beam along the long sides then you are going to have too much sag in the middle of the bed without support legs between the two ends. I have done a lot of design work and worked on a lot of engineered structures over my lifetime so when I look at things such as beds and cabinets then I visualize the loads being placed on the structure and how it will be transferred down to the floor or back to walls or up to roofs, etc. You don't have to be an engineer and get super technical, it will become quickly obvious to the average person if they make themselves think it through.