How to restore files into a new computer

I have a backup of my old dekstop on a WD backup external disk. Now I want to restore those files into my new desktop but when I connect it to the new desktop and install the backup software and click on restore, there are no files and folders there to restore.
It is like it can’t see the backup files from the old computer and is asking for a completely new backup setup.
How can I find those files to restore(I can see them on my file explorer, they are there, but they don’t show up on the app)