FSE: Add basic support for child themes

[Mamaduka]

Description

Part of #25612.
Fixes #33959.
Fixes #33957.

Adds basic support for child themes in Full Site Editor/Global Styles.

Features covered

• Block template and template parts file inheritance.
• The theme.json inheritance.

Props

This is based on previous work by @aristath and @oandregal.

P.S. I'm not sure how we want to handle user-created templates and wasn't able to find any information. I would be happy to iterate on this PR or create a follow-up if anyone can point me in the right direction.

How has this been tested?

1. Create TT1 Blocks child theme.

wp scaffold child-theme tt1-blocks-child --parent_theme=tt1-blocks --theme_name="TT1 Blocks Child"

2. Activate the child theme.
3. See that the "Site Editor" admin menu is visible.
4. Check that you can edit template files.
5. See that template and template parts are correctly rendered on the front-end.

Types of changes

Enhancement

Checklist:

• My code is tested.
• My code follows the WordPress code style.
• My code follows the accessibility standards.
• I've tested my changes with keyboard and screen readers.
• My code has proper inline documentation.
• I've included developer documentation if appropriate.
• I've updated all React Native files affected by any refactorings/renamings in this PR (please manually search all *.native.js files for terms that need renaming or removal).

[carolinan]

Test result:

• The site editor is available when the child theme is active

• Templates and template parts are working correctly on the front and in the editors

• Theme.json is inherited

• Parent theme template parts can be overridden in the child theme

• Parent theme templates can be overridden in the child theme

• Theme.json can be overridden in the child theme

[Mamaduka]

Thanks for the review, @carolinan ❤️