3D object orientation based on plane normal in OpenGL

I am having a problem in 3D to 2D object orientation. So, I am working on an AR app in Python using OpenGL. I can estimate the depth of the scene and calculate the surface normals using other methods. I also have the camera calibration details+rotation and translation. Now the problem is, I want to project a 3D model like a 3D wine bottle onto one of the planar surfaces. The surface can be horizontal or vertical. And, note that the object has to be projected perpendicular to surface. So the idea is that I choose a point by clicking on the surface and the bottle will be projected there. Please see the attached images. One of them is what I have as input and the other ones are the expected outputs.