The reason people say binding is because the words “immutable variable” are an oxymoron. It never makes sense to use variable for immutable bindings; they are not able to be varied. Binding is just the meaning of the word “variable” but without the implied mutability.

This aligns with the fact that the mutability is (syntactically and conceptually) a property attached to the binding, and hence there is a need to talk about bindings generally without implying anything about the mutability. Lots of languages don’t have immutable bindings, all bindings are mutable, so you may as well call them variables in C, Go, etc.