3D plot with custom oblique projection

Question

Orthogonal Projection

I can use the proj_type='ortho' argument to get an isometric projection which will use the following projection matrix:

def _ortho_transformation(zfront, zback):
    # note: w component in the resulting vector will be (zback-zfront), not 1
    a = -(zfront + zback)
    b = -(zfront - zback)
    proj_matrix = np.array([[2, 0,  0, 0],
                            [0, 2,  0, 0],
                            [0, 0, -2, 0],
                            [0, 0,  a, b]])
    return proj_matrix

proj3d.persp_transformation = _ortho_transformation

Oblique Cabinet Projection

Unfortunately I'm struggeling to obtain a Cabinet projection where the x and y axis are horizontal/vertical:

Looking into how a projection matrix would be defined in OpenGL led me to the following code, which results in a very distorted projection:

def _oblique_cabinet_transformation(_, __):

    angle_degrees = 45
    scale = 1.0
    angle_rad = np.radians(angle_degrees)
    
    shear_x = -np.cos(angle_rad)
    shear_y = np.sin(angle_rad)
    
    proj_matrix = np.array([[1, 0, shear_x * scale, 0],
                            [0, 1, shear_y * scale, 0],
                            [0, 0, 1, 0],
                            [0, 0, 0, 1]])
    
    return proj_matrix

proj3d.persp_transformation = _oblique_cabinet_transformation

This is somewhat expected, as the orthogonal opengl exampe already uses a different transformation matrix than matplotlib. What transformation matrix format is this and how do I obtain the desired perspective?