Close the gap to the wall with a cover on the dishwasher

You definitely have to secure the countertop separately to the wall, because it should not rest on the dishwasher.

Actually, the dishwasher is adjusted high enough that the countertop then rests on it. It is practically clamped (beside the screws to be installed afterwards on the right and left into the kitchen cabinets).

I would install the dishwasher completely according to the instructions. First, attach a wooden beam to the wall (with brackets on the wall). Then the dishwasher cannot move sideways anymore. Of course, it must be done with millimeter precision so that it fits tightly. Then, as mentioned, cover the gap with a front panel – that is, attach a strip on the wall side and the dishwasher side (this should work through the screws that would otherwise go into the adjacent cabinet). Then glue the front panel onto it.

If it doesn't, it may move when opening or closing or possibly tip forward when pulling out the basket if it is not properly clamped to the countertop.

That makes sense.

I would install the dishwasher completely according to the instructions. First, attach a wooden batten to the wall (with brackets on the wall). Then the dishwasher can no longer move sideways. Of course, it must be done precisely to the millimeter, tight fit. Then use a front piece as described to conceal the gap – that is, attach a strip on the wall side and the dishwasher side (this should work through the screws, which otherwise go into the adjacent cabinet). Then glue the front piece on top.

Exactly. Wooden batten for the countertop on the wall with brackets, at least then you can glue the panel to it at the top. At the bottom, you can also insert a wooden batten tightly pressed, so lay it on the floor. There may still be a baseboard there, then the wooden batten has to be narrower.

Actually, the dishwasher is turned up so far that the plate then rests on it.

Yes, the dishwasher plate is turned up that far. However, the dishwasher plate is not meant to fully support the countertop; rather, it must be secured to the wall with a bracket or support strip. There is space for that. Then the dishwasher plate can also be pulled out and pushed back in during repairs.

No. I meant it the other way around. The countertop "clips" the dishwasher in.

I have actually never seen a countertop being attached to the wall anywhere before. Whether it's a cheap or a very expensive kitchen. So far, it has always just rested on top or the cabinets were screwed to the countertop from below (if wood, with granite or similar this issue does not apply).

... Just trust me, at the end of a line you don’t simply let the countertop end over a dishwasher without wall mounting or an end panel. That would not be a proper installation.

I have actually never seen a countertop attached to the wall anywhere before. Regardless of whether it is a cheap or very expensive kitchen.

It’s not about a fitted kitchen, but about a way to fix a quasi cantilevered countertop in a DIY manner. By the way, we have it in the utility room: the countertop “hangs” at the end because a small freestanding fridge is pushed underneath there. It forms the end of a small kitchenette. Therefore, a piece of wood is mounted to the wall (instead of a cabinet) as a support. And if I remember correctly, we did the same in the old house with a countertop extension (without a cabinet underneath).