Correctly using inputs_for to update changeset when using embedded_schema

I this example repository I have a very simple form in LiveView at “/” using inputs_for:

MyApp.Parent is an embedded_schema that embeds_many MyApp.Child.
I would like to update these children in a form using inputs_for.

Current behavior:
When I update the changeset the children loses name and age values that were previously set.

My question:
How would I need to change this simple example that the children keep their attributes and only update the selected attribute in the changeset.