https://www.merriam-webster.com/dictionary/paw

Quote:

   Paw : the foot of a quadruped (such as a lion or dog) that has claws

   broadly : the foot of an animal

You obviously sourced this already it just didn't suit your current stance so you avoided mentioning it and instead attacked the veracity of vocabulary.com.

I think among your bat friends maybe they won't call it a paw. But outside of that in other contexts (like here) it's a paw because if fits the definition of a paw in the English language according to the very official source of Merriam Webster.