I am writing the following templated vector class.

vectors.h:

#ifndef INCLUDE_HEADERS_VECTORS_H
#define INCLUDE_HEADERS_VECTORS_H

template<class Scalar> class Vector2D;
template<class Scalar> Vector2D<Scalar> operator+(Scalar a, Vector2D<Scalar> v);

template<class Scalar>
class Vector2D {
    public:
        Vector2D();
        Vector2D(Scalar a, Scalar b);

        Scalar getX();
        Scalar getY();

        Vector2D<Scalar> operator+(Scalar a);        
        friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
        
    private:
        Scalar x, y; 

};

#endif 

vectors.cpp:

#include<headers/vectors.h>

template<class Scalar>
Vector2D<Scalar>::Vector2D() {
    x = 0;
    y = 0;
}

template<class Scalar>
Vector2D<Scalar>::Vector2D(Scalar a, Scalar b) {
    x = a;
    y = b;
}

template<class Scalar>
Scalar Vector2D<Scalar>::getX() {
    return x;
}

template<class Scalar>
Scalar Vector2D<Scalar>::getY() {
    return y;
}

template<class Scalar>
Vector2D<Scalar> Vector2D<Scalar>::operator+(Scalar a) {
    return Vector2D<Scalar>(a + x, a + y);
}

template<class Scalar>
Vector2D<Scalar> operator+(Scalar a, Vector2D<Scalar> v) {
    return Vector2D<Scalar>(a + v.x, a + v.y);
}

template class Vector2D<float>;
template Vector2D<float> operator+<float>(float a, Vector2D<float> v);

Main.cpp:

#include<headers/vectors.h>
#include<iostream>

int main(int argc, char* argv[]){
    Vector2D<float> a(1.0, 3.0);
    std::cout<<a.getX()<<" "<<a.getY()<<std::endl;

    a = (float)2.0 + a;
    std::cout<<a.getX()<<" "<<a.getY()<<std::endl;

    a = a + (float)-2.0;
    std::cout<<a.getX()<<" "<<a.getY()<<std::endl;

    return 0;
}

When I try to compile it with g++ on windows I get the following error:

g++ -Iinclude -Iinclude/SDL2 -Iinclude/headers -Llib -o Main src/*.cpp -lmingw32 -lSDL2main -lSDL2 -lSDL2_image
In file included from src/Main.cpp:2:
include/headers/vectors.h:29:33: error: declaration of 'operator+' as non-function
   29 |         friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
      |                                 ^~~~~~~~
include/headers/vectors.h:29:41: error: expected ';' at end of member declaration
   29 |         friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
      |                                         ^
      |                                          ;
include/headers/vectors.h:29:43: error: expected unqualified-id before '<' token
   29 |         friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
      |                                           ^
In file included from src/vectors.cpp:1:
include/headers/vectors.h:29:33: error: declaration of 'operator+' as non-function
   29 |         friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
      |                                 ^~~~~~~~
include/headers/vectors.h:29:41: error: expected ';' at end of member declaration
   29 |         friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
      |                                         ^
      |                                          ;
include/headers/vectors.h:29:43: error: expected unqualified-id before '<' token
   29 |         friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
      |                                           ^
src/vectors.cpp:70:18: error: non-class, non-variable partial specialization 'operator+<Scalar>' is not allowed
   70 | Vector2D<Scalar> operator+<Scalar>(Scalar a, Vector2D<Scalar> v) {
      |                  ^~~~~~~~~~~~~~~~~
src/vectors.cpp: In instantiation of 'Vector2D<Scalar> operator+(Scalar, Vector2D<Scalar>) [with Scalar = float]':
src/vectors.cpp:96:69:   required from here
src/vectors.cpp:71:35: error: 'float Vector2D<float>::x' is private within this context
   71 |     return Vector2D<Scalar>(a + v.x, a + v.y);
      |                                 ~~^
include/headers/vectors.h:37:16: note: declared private here
   37 |         Scalar x, y;
      |                ^
src/vectors.cpp:71:44: error: 'float Vector2D<float>::y' is private within this context
   71 |     return Vector2D<Scalar>(a + v.x, a + v.y);
      |                                          ~~^
include/headers/vectors.h:37:19: note: declared private here
   37 |         Scalar x, y;
      |                   ^
mingw32-make: *** [MakeFile:2: all] Error 1

However, if I change the order of the declarations of the + operator in vectors.h like in the following it will work just fine.

#ifndef INCLUDE_HEADERS_VECTORS_H
#define INCLUDE_HEADERS_VECTORS_H

template<class Scalar> class Vector2D;
template<class Scalar> Vector2D<Scalar> operator+(Scalar a, Vector2D<Scalar> v);

template<class Scalar>
class Vector2D {
    public:
        Vector2D();
        Vector2D(Scalar a, Scalar b);

        Scalar getX();
        Scalar getY();

        friend Vector2D<Scalar> operator+ <>(Scalar a, Vector2D<Scalar> v);
        Vector2D<Scalar> operator+(Scalar a);        
        
        
    private:
        Scalar x, y; 

};

I am completely lost as to why this happens.

I tried to remove the templates and the problem goes away so it must be related.