Since you want to build it yourself, there are probably no "suppliers". Take a high-performance construction adhesive and bond the bottom slat over the full surface.
P.S. I wouldn’t put up with that visually and would bond the panels on the floor. In my opinion, it looks bad from the back side. And if properly heavy cupboard elements stand on the floor, nothing should slip (the panels are also screwed into the ceiling).
Actually, I would find it visually better to fix individual panels without the large slat on the floor to which all the panels are attached. That would look much more delicate in my opinion. The disadvantage would be that I have to fix each individual slat with plastic profiles on the floor and also on the ceiling. I don’t know what that looks like either...
What do you mean by "looks bad from the back side"? In which construction? When fixing with plastic profiles?