Should the refrigerator be freestanding or integrated?

If both are standalone devices, you can take whatever you want. You just have to be careful if both are to be installed one on top of the other, that there is a bit of air between them. The necessary air can be found in the manual and can best be controlled by the countertop thickness.

Can someone maybe finally explain to me what it depends on whether the cooktop and oven fit together? So you can buy proper sets or both separately... But I have already read several times that both have to match... But how do I recognize that! ^^

If the two stand separately, they don't have to match. Nobody recognizes the oven's manufacturer when walking by

No, they are already together with us because we are not building the oven higher, but the dishwasher. Therefore, the oven and cooktop must already match...

That does not necessarily mean that you need a hob set. You can also install independent appliances stacked on top of each other (if there is enough space—induction cooktops in particular sit slightly deeper) and then they have nothing to do with each other. If the cooktop control is via the oven (i.e., a hob set), I would simply take both from one manufacturer; they should be compatible. Or is there a specific reason/device preference why you don’t want that?

No, not at all. My thought was just that when you mix and match freely, you can find a good oven and a good cooktop, whereas with a ready-made set you probably have to make a compromise with at least one appliance...

We will also get a country-style kitchen and have treated ourselves to a freestanding American fridge placed centrally in the middle of the kitchen....

However, this will be integrated by the kitchen builder......on the left and right it will be surrounded by a thin drywall and above it a shelf made of wood......many country-style kitchens I have seen online still have a bulky silver fridge inside despite the style.....