Also, other comments here speak of “separating into the voice and accompaniment,” so maybe the model/program already do exactly what you need.
When you have an instrumental version of a song (from the same stems as the vocal version) this is already one way to get the vocals out without any fancy machine learning. The main tricks besides what you can do in Audacity like that are properly time-aligning the tracks (even if they drift a bit) and compensating for phase issues and compression. I wrote a dirty tool that does that and I've been meaning to turn it into some kind of nicer GUI version.
Or you can do the exact opposite and instead of center channel extracting the vocals you can remove the vocals and use this method to better isolate vocals.
Although if things do fun stuff with stereo it might not be exact.