Okay guys, shame on me - it was my fault.
I found out by chance. I use a stream deck when I play DCS. It's usually on the desk on the side. When I start DCS, I put it right in front of me. When I do that, the USB cable stretches a bit and puts pressure on the USB cable of the external sound card behind the computer. This causes the USB plug of the sound card to move ever so slightly to one side (inside the connector), which leads to occasional short interruptions - and that is why DCS then switches the sound output.
When I put the stream deck after my DCS session back, the USB cable relaxes a bit and thus no longer touches the cable of the sound card.
Therefore, the problem only occurred while playing DCS. 😬
Airbusjoerg's post in DCS suddenly changes the sound source during runtime was marked as the answer