Why does file transfer show no files or folders on a connected & controlled android tablet?

you need to open teamviewer "host" app on the device you are controlling. IF the host app is opened when you are starting the file transfer tool on teamviewer from the controler device, the controlled device will pop up a message asking for permissions for all files on the device. After you grant those, everything will work fine.
Alternativly you can manually search for the grant file access to all files option in your android settings (I don't know the exact wording in English) and then grant the access to all files to "teamviewer host app".

Thats it.