Transfer game to child account

you can indeed transfer money from a parental account to a child account, can be done accidentally too, not sure if there is a way to transfer back as child account cannot transfer money.

You can't downgrade or transfer an adult account to a child account

Your best solution would be to make a new child account and use the home setting feature to share games

You can create a child account on your current parental account. You can not transfer games, saved progress etc. You can set the parental account to Home Xbox and the child account would have access to the games but not the saved progress.

It is not Microsofts fault that a child account was not set up.

No, it's not possible to transfer game progress from one account to another. Your child will have to start the games again on his account.

There is no way to make an adult account into a child account. You would need to create a new account as a child account for him to use and then your account would be the parent account that oversees it. There is no way to transfer any achievements or
game saves to that account.