If there’s any checking of types before program runs then it’s static typing. Gradual typing is a form of static typing that allows you to apply static types to only part of the code.
I’m not sure what you mean by variables not changing types during execution in statically typed languages. In many statically typed languages variables don’t exist at runtime, they get mapped to registers or stack operations. Variables only exist at runtime in languages that have interpreters.
Aside from that, many statically typed languages have a way to declare dynamically typed variables, e.g. the dynamic keyword in C#. Or they have a way to declare a variable of a top type e.g. Object and then downcast.
