Like a lot of biology, it’s complicated and often you need multiple forms of evidence to support a species classification if the viable offspring (biological species concept) doesn’t suit.

So there are lots of different models for different types of organisms. And some reproduce asexually so reproductive compatibility would never be enough.

Two simple options are evolutionary lineage (effectively genetic distance) or physical characteristics (morphology): https://bio.libretexts.org/Courses/University_of_California_...