yes, the phone is connected via WLAN into the same network.
Well I am using a repeater (fritzbox) this could be an issue, I will try out without the box.
As I told before I can see all the devices if I connect through the computer but this is not working systimaticely. After I killed/closed and restarted the spotify App I could find it again on my computer, but just for a short laps of time (maybe 20 sec.).
Thank you for the advice, I will continue trying out and maybe come back to you if I have some new interesting details.