Update for all those who experience the same problem in the future:
I did sudo chmod 777 on one folder and then created a new folder via the webinterface. From there I saw, that the permissions from the newly created folder were the following:
drwxr-xr-x. 2 33 tape 4096 Dec 28 16:30 test
Notice the 33 tape? This is it. Afterwards I just did the following on my external ssd and it worked:
sudo chown -R 33:tape /media/krane-cloud/
Remember to sudo chmod 755 again on the folder you gave 777 permissions earlier.