It’s a bit hard to understand the functionality you’re after… but are you just wanting to be able to switch between the Pi streamer and your DJ rig as your playback source, going to your monitors? If so, you would do that by just adding a separate switcher.

https://www.amazon.com/Nobsound-Audio-Switcher-Selector-Splitter/dp/B07875KC4F

Like this for instance. Or one of the other Nobsound/Douk switchers… they make several, with slightly different layouts.

Or you could skip the Pi solution and instead just get a retail streamer that includes line inputs. The Wiim Pro or Arylic A50 Pro+ for example.