Scrivener has one Theme per entire application, so saving a Theme per Document or even per Project is not supported. When you change a Theme it’s for all Documents and all Projects.
Although Backgrounds are part of Personal Preferences, AFAIK they’re not saved with the Theme. You could try saving your Preferences in File > Options > Manage and see if Backgrounds are included…
The difference between Load Theme from file and Importing Themes is that the latter is copied to the application’s Themes folder and the former are not. The imported Theme appears in the menu with the build-in Themes.