Actually, a recent study -- https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0254175#abstract0 -- from 2021 found that

Neanderthals had a set of genetic variants which would have made their children susceptible to a rare blood disorder called Haemolytic Disease of the Foetus and Newborn, or HDFN. A result of HDFN is a fatal kind of anemia, and the affected generations would have had trouble reproducing — ultimately eliminating their bloodline.

This suggests it wasn't just violence or rivalry between our two species that led to Neanderthal extinction, but also potentially, attempting to breed with H. sapiens!