Audacity has two algorithms for separating sources.
The simple type can be seen in “Vocal Remover” (https://manual.audacityteam.org/man/vocal_remover.html). This works by inverting one channel and mixing with the other channel so as to cancel out sounds that are panned centre (common to both channels).
The other type can be seen in the “Vocal Reduction and Isolation” effect (Vocal Reduction and Isolation - Audacity Manual). This uses FFT analysis to find sounds that are common to both channels, and can reduce them, or (partially) isolate them.
This came up a while back in this topic: Reduce voice not eliminate
The software referred to is available on GitHub: GitHub - wslihgt/separateLeadStereo: Separate the lead from the accompaniment, in polyphonic audio music excerpts, in Python/Numpy