Maybe the lesson for children should be less about how to use tools to manage a password, and more about understanding why managing passwords is important?
Let them write their passwords in a notebook. Have fun with devising a method for obfuscation in case the notebook is lost. Teach them about backups- keeping a copy someplace safe. In my experience, kids and old people are a lot alike when it comes to password (mis)management
Until they were skilled enough to manage their own passwdpassword database, iI also kept the kids logins in a "family KeePass". This is the same one where the aged family members stuff is- because people die and sometimes you need to recover things for otherwise unable people. The trust/risk calculus is different in a family group than in a work or social circle. There is also a difference between sharing access to a password and sharing a password.
It is awesome that you are thinking about this early. goodGood luck!