VSCode says std::chrono is ambiguous if operator<< overloaded

I have an overloaded operator<< for std::chrono::duration. As I understand it I have to put that in the std::chrono namespace so ADL works. However, for some reason when I do that all other references to std::chrono::duration get marked as ambiguous by VSCode. This might just be a VSCode bug but it uses clangd to do correctness checking so I'm wondering if there is actually something wrong with my code. It does compile but VSCode isn't using exactly the same clang as I'm compiling with so maybe mine is just more permissive?

The smallest example I could come up with is:

#include <chrono>
#include <iostream>

// marks chrono as ambiguous
using std::chrono::milliseconds;

namespace std {
namespace chrono {

// again marks chrono as ambiguous
template <class U, class T>
std::ostream& operator<<(std::ostream& os, const typename ::std::chrono::duration<U, T>& dur) {
  os << "foo";
  return os;
}

}  // namespace chrono
}  // namespace std

namespace example {

void DoThing() {
  // NOT marked as ambiguous
  milliseconds x(10);
  // Says no match for operator<< and milliseconds
  std::cout << x;
}

}  // namespace example

Does it look to anyone like this isn't valid C++ or is this more likely a clangd or VSCode bug?