In Switzerland, registration is mandatory for all drones weighing 250g or more or if they have a camera or other sensors for data acquisition, i.e. pretty much everything except toy drones. You must register as an operator and then affix this number to your drones. Stickers or by hand is simply legible.
Drones weighing less than 250g do not actually have to be tested, but the A1/A3 licence can be obtained very easily and free of charge online from the FOCA.
The Mavic 3 PRO discussed here is a C2 drone so at least the A1/A3 licence is mandatory and if you want to get closer to the interesting motifs you need the A2 licence, currently also free of charge but you have to take the exam on site and learn a little more (also no big deal)
STICK TO THE LAWS! FLY WITH COMMON SENSE!
We now have a legal basis that everyone can live with, and it is valid throughout Europe, including Switzerland and Norway. It will only stay that way for so long

I cannot answer the question about drone registration like in Iceland but in Switzerland a certificate is needed, including insurance, to fly this drone.