Or indeed smaller, as mine was (at least I could cut the hole bigger).

As the OP said "old ... tap" any assumption about standardisation is very risky, particularly in the world of Swiss kitchens.

The base on our existing faucet is quite wide, compared to the faucets I've seen being sold on amazon.de (which list the diameter, etc. in their descriptions).

I measured the circumference of our existing tap's base, and it's 17.78 cm (converted to cm from 7 inches), so then from that I divided by pi / 3.14 and got a diameter of 5.662 cm.

Many of the faucets I've seen being sold have a much smaller diameter than that, and of course I can't really see how big the hole in the countertop is unless I remove the old faucet, which I'm not willing to do until the new one is here and is being installed. Being that we rent, cutting a hole is not an option. But hopefully the landlord will be willing to install a faucet of our choice if we purchase one. The problem is going to be finding one that will fit, I guess.

Can't you look underneath? You should be able to see the size of the threaded part of the tap from there. It will almost certainly be significantly smaller than the part you see above.

Thanks! That is an excellent idea. I'll try to crawl down there tomorrow with a flashlight. Thank you again.