The Basal Eurasians are to archeogenetics what dark energy and and dark matter are to cosmology. If we can't explain something, let's just make up a new force, form of matter or, in this case, a ghost population. The BEs are defined by the lack of Neanderthal admixture, yet no sample of this proposed population has been discovered so far. I would argue that there was a bigger diversity of different hunter-gatherers in the Middle East. Some papers mention a "West-Eurasian Unknown HG population" or "Unknown HGs" (another made-up category) but there is a case for a far greater diversity of genetically distinct groups, at least in the Holocene.
The tree that bicicleur 2 posted is from this paper:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10781627/
I don't claim to be qualified to pass a judgement but it doesn't look like they discovered anything new. But hey, you gotta publish as much as possible to justify your existence.