C++ Concepts - Can I have a constraint requiring a function be present in a class?

You are testing for presence of a static member function. What you want is

template <typename T>
concept bool HasFunc1 = 
  requires(T t) {
      { t.func1() } -> int;
  };

Try calling it yourself:

Test::func1();

prog.cc: In function 'int main()':
prog.cc:19:14: error: cannot call member function 'int Test::func1()' without object
   19 |  Test::func1();
      |              ^

Oh, right. func1 should either be a static member function, or you should call it on an instance inside your concept:

template <typename T>
concept bool HasFunc1 = 
    requires(T t) {
        { t.func1() } -> int;
    };