I am using the Car Repair Pro Theme. The Media Library is not populated when I e.g. try to customise the site identity logo. Also, uploads to the media Gallery are not possible.
If I try the same with the standard Car Repair Theme (the free version) everything works as expected and I see the Media files.
Also, I can see the Media files if I access the Media folder in the directory on the main wordpress control panel.
Thank for pointing me into the right direction!