Whether or not something belongs into a type system is ultimately determined by the type system. We can choose whether or not mutability is considered a part of a type.
> When we speak of "type of a variable", we mean this variable can only be assigned (bound to) values of certain type. This has nothing to do with whether it can be reassigned (i.e. mutability).
This is a bit too simplistic IMO. You're talking about name bindings, the article is talking more about things like interior mutability.
Rebinding a name is ... generally not a type system concern by my understanding.