There is no completion for static methods or variables.

class Foo {
public:
    static void bar() { }
    void blubb() { }
    
    int x;
    static int y;
};

int main(int argc, char *argv[])
{
}

No completion after typing e.g. Foo:: in main.
There is completion for variables of type Foo though, Foo f; f. shows completion.