@join Thank you very much for your input! The powerbank was the right tip!
So with the 3-in-1 adapter, a powerbank and a Y-cable it now works.
I had to plug-in the headphones to the adapter and connect the adapter to the iPhone. Then connect the additional power supply part of the Y-cable with the powerbank, the Y-cable with Sylphyo. Then plug in the Y-cable with power and sylphyo to the adapter.
After doing so I could start Audiobus app and play a software synth (Respiro) with my Sylphyo and a play along over my headphones :-)
All in all it’s not the sleekest solution, but hey - it works.
Thanks again for your support,