Mathias,
I’m sorry about this noise problem. This problem has to do with some of the PWM frequency leaking into the ground path of your power supply. Certain power supplies, (mostly regulated switch mode power supplies) don’t have much filtering on their output, so these frequencies can leak into the audible part of the circuit. Other power supplies (like linear powers supplies) help filter these frequencies out of the audio path. You can verify that this is a power supply issue by using a battery to power up the Quaverato (with a 9v battery snap to barrel adapter). So one thing you can do is try a different power supply. I recommend using a linear power supply for this application.
Another thing that you can do is add a filter capacitor across the microcontroller as described in this post: https://zeppelindesignlabs.com/forums/topic/extra-noise/page/2/#post-25412
This capacitor helps filter the frequency at its source.
Another thing you can do is make sure all your solder joints are not too large and then clean off the flux from the circuit board (as described in another post on that same forum).
I hope this is helpful for you. Please let me know if you have any other questions.
Good luck.
-Brach