I do actually select “Exit”. The Classic UI is then up. But after some time I restart OSMC manually and OSMC-UI is enabled so Classic UI has to be rechosen again.
This is still reproducable as described above with current 2019.07-1.
This is what I am thinking as well. I am not aware of any skin that goes by the name “Classic” and it is not in the official repo. It sounds like you may have manually installed an old skin that does not have support for the current version of Kodi.
With “Classic” skin I actually mean Kodis default skin “Estuary” which is not an unsual skin I guess. This is by default integrated into OSMC (during install one can decide between OSMC skind and “Estuary”).
I will try to upload logs after during a clean install.