bought Xbox game on parent account for child account and child can't play

Just to clarify SMw means to set your sons Xbox as your home Xbox. That also means he'll be able to play any anf all your games FYI.

You'll want to set the console as your Home console. https://beta.support.xbox.com/help/hardware-network/console/my-home-xbox

You can't transfer licenses or content from one account to another.

The accounts Parent / Child are separate accounts. The parent account just manages the child account.

The child account will remain a child account until the birth date that was used for that account reaches the age of 18.

Once you register an xbox live account as a child account you can't change it. The parental account can change privacy settings of the child account though.

Hi. My name is Brilliant, an independent advisor. I am happy to assist you today.

Parent and child accounts on Xbox are designed to help parents manage their children’s gaming activities. A parent account is the primary account that can create and manage child accounts. Child accounts are created for children under the age of 18 and are linked to the parent account. The parent account can set up parental controls, such as screen time limits, content restrictions, and spending limits, for each child account.

You cannot change your account to be a child account. You will have to create a new account for your child.

To create a child account, the parent account must first create a family group. The family group can have up to six members, including the parent account. Once the family group is created, the parent account can add a child account to the group. The child account will be linked to the parent account and will have access to the parent account’s Xbox Live Gold subscription and other benefits.

I hope this helps.