The theme DOES NOT control the settings for the logo, the header image or the background image.
The logo, the header image and the background image are controlled by the core WordPress files.
You can see this because the theme does not have Russian translation for the customizer options, and you can see that the customizer settings for the logo, the header image and the background image are in Russian language because the core WordPress installation does have Russian translation for the core logo, header image and background image settings.
There must be something else that has removed your saved options for the images, because these settings are not controlled by the theme.
To rule out a plugin conflict, please can you temporarily deactivate all plugins, then try to add a header or background image.
If it works correctly, then reactivate plugins one at a time until the problem reappears. By doing this you will be able to see if it is a plugin that is causing this problem.