How do I treat "Library"?

Its content is one of OS’s mysteries. As far as I am concerned “Don’t touch it!!”

Is that correct? If I look at what “WhatSize” shows I get second thoughts. Do I really have to keep everything?

Generally speaking, yes, leave it alone. What you highlighted are backups of your iDevice on both iCloud and iMazing. You can probably reduce their sizes from within iCloud settings and the iMazing app if there are multiple backups there that you no longer need. Deleting them directly from Library may corrupt things and prevent you from restoring a backup should you need to.

Thanks for this. Looks like I’m suffering of a case of “over-backing-up”, the main symptom being “I’m loosing control over what is where”.