Hello,
I am trying to use KDEConnect for backing up my phone (Android 8, Sony Xperia) to my laptop Kubuntu 19.10. I can easily transfer individual FILES but not FOLDERS. When trying to "select all items" on the phone, only files but no folders are selected. What might I be missing?

It may be a limitation of your file browser, or perhaps Android?
Try it the other way, by opening the phone in Dolphin. Kdeconnect should put it on the sidebar. Copy folders from there to your PC via drag and drop or copy-paste.

Thanks for your quick answer!
I have found the solution to the "problem": My phone was not connected through USB. When I connect it in that way, everything I am allowed to see (non-rooted!) shows up alright. I am also using adb now for backing up. Greetings from Salzburg H.S.