Oh, I had assumed that it simply means it is somewhere under the countertop, not directly beneath it. But you're right - whether it's above or below probably doesn't really matter.
With the "base cabinet with waste system," it's mainly about being able to sweep the waste directly from the work surface, e.g. from cutting vegetables, straight into the organic waste bin without having to carry it somewhere else. I prefer the lighter wood; I can't quite get used to the dark brown countertop. I also like the version with the continuous row better than that kitchen island you have.
It is so practical, just like the raised dishwasher, there is nothing practical in everyday life, really. Just tonight I had to load and unload it twice...
I don't think the solution with the peninsula you have is wrong at all... somehow the right walking paths. But I would really put the dishwasher opposite the sink in the corner, at least slightly elevated with a pull-out. And under the countertop next to the sink, the base cabinet with the waste system can go. You will certainly do a lot of preparation here because the refrigerator is also directly next to it.