But it doesn't have mammary glands(boba) , Notochord , lungs or not even a 4 chambered heart
Well, they do make milk, mammals don't have a notochord anyways.
You are correct, but it is also correct that taxidermy is very arbitrary.
Like obviously plant and animals are different, but apart from what a species is, we really don't have any clear cut definition of things.
You can check if two things are of same species by marrying them and seeing if they make healthy reproductive babies.
But what is genus? It's just, "these two species look similar, so I am gonna group them"
Same with family, order and other stuff all the way to kingdoms. It's all just, "these things look similar so they must be in the same group "