Parent to Child Reference Field

When making relationships between parent and children records I understand how to add additional lookups. But when you do that then those fields need to be "updated" when adding a new child. What I am seeking is a way that when a child record is created, and related to a specific parent, that the child record would show the value of additional fields from the parent.

Example:

Parent record has Name, Address, Phone Number, Favorite Color

Child record has Child name, lookup field to select parent which would bring down the Parent Name and Favorite Color

Currently when setting the relationship I would connect on Related Parent then add the lookups for Parent Name and Favorite Color, but when actually creating the new Child record once I select the related parent, the Parent Name and Favorite Color are not populating. If I want those to display the value, I have to manually update those fields (thus not benefiting from setting the relationship to the Parent).

What am I missing? This seems like an easy ask but for the life of me I'm just not seeing a pathway to make this work.