Update: It worked even less there but only to the extend that i had to set the fairphone up as an adb/fastboot device in the device manager first. When that was done the outcome was the same as befor on my laptop.
I will check the exact version it would be my kind of luck to have an outdated version on my tower and a broken version on my laptop.
Is this the correct menu. The phone shouldnt not show up as a fastboot device but still.