Today I had some spare time. I liked to follow the last clue of peter_watt I didn't tried so far.
My iPad, stil on iOS 13.5, has the same issues as many people have and as I have on my iPhone Xs.
I don't use my iPad that much, so I can try some things on that appliance.
First of all, I did a DFU restore, but I didn't set back an iCloud backup-copy.
With a "virgin" iPad, just install one app what's always running in the background: Buienalarm.
I came to look one hour after opening Buitenalarm and yes, again: 60% used in background when it's not supposed to do so.
Another story: I've told the whole story to my wife, with the target not to upgrade her iPhone 8.
She didn't know iPadOS and iOS are practically the same. Her 1/2 year old iPad 2019 is upgraded to iOS 13.5.1. She uses completely different apps as I do, but the same issue on her iPad too.
Also hardware faults on my iPad and my wife's too? I don't think this problem can be solved :-(