Can I save this tree?

Hi there

I'm new to this forum, so not sure if I've placed this question in the correct section.

I have two trees which I believe are magnolia, but I could be wrong (if so, I'd love to know what they actually are). They are always green with no flowers.

Unfortunately, one of the trees got damaged by a digger while getting work done on our house a few months ago. It was pulled right out of the ground by the digger, but we immediately planted it again and held it up with supports.

However, the leaves have turned yellow/brown and it just doesn't seem to be doing as good as the other one which we got at the same time. As you can see in the photo, they look very different. The healthy one is very full and fresh looking, while the damaged one is looking very sparse.

Is there anything we can do to help it come back? We are devastated this has happened.

Any help will be greatly appreciated.Thank you