Template parts: use WP_Theme_JSON_Resolver_Gutenberg instead of WP_Theme_JSON_Resolver

[oandregal]

What?

Updates the templates screen to use the bundled Gutenberg class instead of the core one.

Why?

The bundled Gutenberg class may receive updates in the plugin, so we need to use it instead of core's.

Testing Instructions

Introduced at #42729

[spacedmonkey]

Instead of making changes like this, can we work on changing core to make it filterable.

Something like this.

function get_wp_theme_json_resolver(){
    $class_name = apply_filters( 'wp_theme_json_resolver_class', 'WP_Theme_JSON_Resolver' ):
    return $class_name;
}

[github-actions]

Flaky tests detected in e5f83e5.
Some tests passed with failed attempts. The failures may not be related to this commit but are still reported for visibility. See the documentation for more information.

🔍 Workflow run URL: https://github.com/WordPress/gutenberg/actions/runs/4467373574
📝 Reported issues:

• [Flaky Test] can detach blocks from a template part #42245 in /test/e2e/specs/site-editor/template-part.spec.js

[aristath]

I agree that ideally, we'd be able to change this globally, but until that happens I think this PR looks good and is safe to merge, allowing us to wok in Gutenberg until Core gets patched for this 👍

[Mamaduka]

Thank you, @oandregal!