Depends on the context of the story. In this story, no, it wouldn't be either. "Furry" refers mainly to the anthropomorphized version of animals, so that doesn't apply here. And I wouldn't say this counts as beastiality because a, they are a human figure, and b, are being portrayed as having human reasoning.
That said, without knowing the context of that it was an animal beforehand, if that isn't disclosed first before any romance/adult pursuits happen, I would say that's a different breach of consent. Just because it's not outright either doesn't mean it wouldn't cross the boundary of what's acceptable for some people. I don't think this is meant to be particularly nuanced or thought provoking but I didn't get very far before deciding this wasn't for me.
If an animal become human, and a true born human falls in love with the said animal-turned-human... does that count as a beastiality/ furry??? I mean the animal is human as of now but it was an animal before, not reborn but turned into right after
Help I keep thinking about it after reading second chapter and it's been bothering me the question is just stuck in my mind