@davescm can answer that better when he sees this. He's our local 3D wizard 🙂
Thanks for the tag Dag.
The alternative to painting would be to use a 3D modelling and rendering application such as Blender 3D, 3D Max, C4D or similar. It would involve creating a 3 dimensional computer model of the furniture which could then be treated in one of two ways.
a. Texture the model furniture item and the floor, light them then render both as a complete 3D scene.
or
b. Do not texture the model, but just light it. Then render with the model invisible to the camera and a plane on the floor acting only as a "shadow catcher". A shadow catcher in a 3D application only shows the rendered shadows and is otherwise transparent. This render of the shadows can then be combined with your original image to add in a realistic shadow. Of course this relies on matching the original camera angle, distance and lens. There are tools to to this in 3D - e.g FSpy for Blender.
Either of these options involve a considerable time investment in learning how to model and render in your chosen 3D application. For occasional use you may be better of just painting in the shadow by hand.
Dave