I have a problem with rendering the background image. I have two characters and added a background image. In rendering, only the characters get rendering and no background image. I spent two days of trying to figure out what is the problem and I couldn’t find any. I checked the transparent, and added the nodes.
So, your approach is a little off. You have two Composite output nodes, and as the manual says (https://docs.blender.org/manual/en/latest/compositing/types/output/composite.html#outputs):
If multiple Composite nodes are added, only the active one (last selected, indicated by a red header) will be used.
You have two Composite output nodes, and your background is not connected to the node tree that leads to the active (red header) one. I’ll try and mock up what it should look like for you.
Edit:
I recreated your node tree. It should look like this:
