Apple Pencil app without any analytics or syncing or network use
Apple notes is the clear defacto standard for this use case.


Don’t turn on iCloud syncing for notes or don’t sign in to iCloud and you have pretty much all the items you mentioned. 
If you have iCloud backups, by default that does save your content. However if you disable notes to backup, Apple documents that they delete your copies in the cloud when you elect to not back up that data so even if you mistakenly allow that, you should have reasonable control over your data retentionand know what to expect.