I am not familiar with the habits of your squirrels in Denmark, but here, Rocky Mountains of Western United States, squirrels cause an extensive amount of damage.
Where they will go through and shred bark for nesting material, this is usually from shreddy-barked trees such as Tilia, Thujas, and Populus. Damage caused by this activity will appear as scratches on the bark, different from your photos.
The real damage occurs with their chewing. Which looks exactly like your pictures. They don't do this just to sharpen their teeth. They like the taste of the young cambial tissues of some trees and once they find a tree they like, they can really hammer it.
We have seen serious flagging in Norway maples and upon examination found entire limbs, up to 4" in size completely girdled by chewing.
Dave