A normal sim fits, and not an e sim, because with the physical one you can change suppliers abroad....

In principle (i.e. in terms of physical size and connections) you can use any normal SIM, unless it is a Galaxus SIM! They explicitly do not work in routers. They are so heavily throttled on the network side that practically nothing works as soon as the network recognises that the SIM card is in a router. Unfortunately, I had to learn this the hard way after a router with a Galaxus SIM failed to work after having worked for years with a Sunrise SIM. Apparently it's part of the deal between Galaxus Mobile and Sunrise (whose network Galaxus uses) that the SIMs cannot be used for mobile routers.

If you use a nano-SIM on both devices, you can switch back and forth.

In principle, you can use the same SIM. So that you don't always have to switch SIMs back and forth, there are telecoms providers that allow you to use several SIM cards (with the same phone number but a different SIM card ID) at the same time. If you have an unlimited data flat rate, as in my case, you don't pay any traffic charges. I use my Nighthawk as a back-up for my home network. When I go abroad for a longer period of time, I get a normal SIM for tourists and the router becomes my permanent companion. As I also fly a drone, I can connect the remote control to the Nighthawk.

Regarding my own question: Galaxus Bot immediately confirmed that I could indeed use a normal SIM card and switch it back and forth between my smartphone and the Nighthawk M3 router, if this makes sense. I'm still asking the Community if there's more to know or if there are any concrete experiences for such a use case.