[itsme]

Thank you for all your proposals. I have alternatives enough to do all I need:
1.) TotalCommander for Android with its plugin TotalCmd-LAN on the tablet to access shared folders in the local WLAN via SMB
2.) FolderSync to synchronize folders on the tablet with folders in the local WLAN (SMB again)
Both is pretty slow when I need to copy my 800+ MB backup files from the tablet to the PC. So for that I use
3.) MyPhoneExplorer's file transfer via USB cable. It is installed on the PC and uses ADB (Android Debug Bridge), so installing an ADB driver on the PC and activating USB-Debugging in the developer options of the tablet is required.
4.) My tablet supports USB OTG so I can plug a USB stick into an adapter and copy files to and from it. Not what I use every day, but helpful in certain cases.

What I am looking for is a better understanding of MTP. This is what today's tablets and PCs pretend to support out of the box without any further apps and installations. Thank you for the hint: after restarting tablet and PC all the files are visible. WTF is going on here?

In the good old days of prehistoric Android 2.x USB mass storage (UMS) was common. I could plug a phone into a USB socket and it worked. Recently a friend asked me how he could transfer his scores to the tablet and I had to answer "without a thourough investigation of your Android version, your local network, the brand of your tablet and several other facts I can't tell for sure, probably you'll have to search and install additional apps"