Thank you so much everyone for all the ideas. I went on a call with Apple but that support level wasn’t really helpful as he just suggested switching backup off and on again or setting up the iPhone again as new iPhone via Mac.
I then dabbled with the settings again and deselected some apps to be excluded from the backup - even though all apps together were only 1/100th of the supposed total backup. Either way, this dabbling must have provoked iCloud or the iPhone or both to reassess the backup and the backup finally went down again to a normal to be expected size of 6GB 
.
This has been steady for the last days and all seems to be fine again.
Nevertheless, as suggested I created a local backup of her iPhone in iTunes, Music, Finder … ah wherever 
. Better be save than sorry 