One thing to test, just to rule it out, since I had noise issues at first.
More specifically this part:
Ps. At first I thought that something else was also broken, because once the relays started working again, I experienced a high pitched whine when connecting a guitar to Input 1. There was no noise when using the Input 2.
But after a lot of additional troubleshooting I found that the CV/Expression port was set to CV by default. Switching this to Expression pedal (with nothing connected to it physically) removed the whine completely. Interesting, but I guess there was some interference creeping into Input 1 when this was set to CV without anything connected in that socket.