Granted, this was probably a little more controversial when I was doing my undergrad, and the Neanderthal Genome Project stuff was just coming out (at the time, the evidence of Neanderthal DNA in AMHS was seen as a strong confirmation that the two groups met the definition for a single species under the Biological Species Concept), but like, this article
https://www.geneticliteracyproject.org/2014/02/04/were-neanderthals-a-different-species/
Which you almost certainly read during your cursory search; says that it’s still controversial. Like, there’s some evidence that some hybrids might have been infertile, but there’s also definitely evidence of admixture, meaning there was evidence of fertile hybrids…there are taxonomical differences, but determining species by taxonomy alone is always sketchy…and there’s an argument to be made for an ecological species concept, but that would require a lot of data that we don’t have.
When it comes down to it, the definition of “species” is pretty fuzzy, and Neanderthals/AMHS appear to be kind of an edge case. It’s also very important to remember the political history here, and that there has always been a strong urge to categorize Neanderthals as “inhuman” non-ancestors of Europeans (in favour of frauds like Piltdown man, for example) due to their perceived primitivism.
PLUS there’s a whole thing where anti-racists became highly opposed to multiregionalism for reasons which were in part political, which muddies the water even more.
My overall point is that the fact there was cultural exchange between AMHS from Africa and Neanderthals isn’t cool solely “because they were different species”, since their level of interaction and cultural exchange is actually a datapoint in an ongoing debate about whether or not they should be considered different species in the first place.
–Peter