Template part does not save to child theme, but parent theme.json does

This is may be related to #67.

When I save changes to a child theme:

• changed templates save as expected to the child templates folder
• but changed template PARTS save to neither child nor parent, but are nonetheless removed from database, and lost

Also, the entire parent theme.json is saved to the child theme.json, which is not what I expected.

I expected only the differences to the parent theme.json to be saved to the child theme.json.

In my case I had only a new color palette in my child theme theme.json, so I expected that upon saving, the child theme.json would still have only the child color palette and nothing else.

My limited understanding is that on page load, objects in the child theme.json overwrite objects in the parent theme.json? If so, my concern is that any later update to the parent theme.json will no longer be visible because a prior version of the parent will have been copied into the child.

Start by reproducing the child-theme save flow described in the issue, comparing changed template parts with changed templates in the child templates folder. Inspect how the parent and child theme.json files are handled during saving and verify database removal behavior. Done means template parts persist and child theme.json contains only child differences, preserving later parent updates.