block-based child themes don't inherit a parent's theme.json, which is one of the barriers to parent/child themes.
Unfortunately class-wp-theme-json-resolver.php doesn't have any filters, but we might be able to use WP_Theme_JSON::merge(), or overwrite some global until official support is implemented.
Alternatively, we could assist with WordPress/gutenberg#27305 if we feel like it'd be worth it to start with a parent/child structure from the beginning.