I think this article has an interesting, nuanced take.

https://www.nhm.ac.uk/discover/are-neanderthals-same-species-as-us.html

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A few interesting pieces of information:

• Neaderthal and Homo Sapien do not have 1 common ancestor directly before the "species" / "population group" / <insert whatever vocabulary word you want>. Actually, they don't share a common grand-ancestor. The divergence is older than 2 grand-ancestor speciations.
• There are other examples of hybridization, some of them produce fertile offspring. We still consider those original individuals as distinct species. https://www.smithsonianmag.com/science-nature/animal-hybrids-ligers-and-tigons-and-pizzly-bears-oh-my-31133439/
• The latest estimate is that 16% of all bird species interbreed in the wildhttps://onlinelibrary.wiley.com/doi/abs/10.1111/ibi.12285
• Lastly, biological species is a word that predates a LOT of genetic research. Due to the lack of information, the definition is lacking - however, the difference between animals can still be significant even if interbreeding can occur. Tigers and Lions are definitely different animals - huge behavioral changes in terms of hunting, mating, social structure. Consistent differences in size and athleticism
• Species was first used in 1686, it's an outdated term and associated definition. It probably isn't very scientifically accurate, but we need to actually find the right balance. https://en.wikipedia.org/wiki/Species_concept#:~:text=Before%20Darwin,-The%20idea%20that&text=The%20term%20species%20was%20just,was%20possible%20within%20a%20species.