Try setting the wp_theme term again

lib/compat/wordpress-6.8/template-activate.php

@@ -87,29 +87,28 @@ function gutenberg_pre_get_block_templates( $output, $query, $template_type ) {
 	return $output;
 }
 
-// Whenever templates are queried, include all templates, not just the ones with
-// a matching theme. See:
-// https://github.com/WordPress/wordpress-develop/blob/94a798b54b4be308cfafb2db09bbed9c3ea9ff34/src/wp-includes/block-template-utils.php#L1111-L1117
+// Whenever templates are queried by slug, never return any user templates.
+// We are handling that in gutenberg_pre_get_block_templates.
 function gutenberg_remove_tax_query_for_templates( $query ) {
 	if ( isset( $query->query['post_type'] ) && 'wp_template' === $query->query['post_type'] ) {
-		$query->set( 'tax_query', array() );
+        // We don't have templates with this status, that's the point. We want
+        // this query to not return any user templates.
+		$query->set( 'post_status', array( 'pending' ) );
 	}
 }
 
 add_filter( 'pre_get_block_templates', 'gutenberg_tax_pre_get_block_templates', 10, 3 );
-add_action( 'pre_get_block_template', 'gutenberg_tax_pre_get_block_templates', 10, 3 );
 function gutenberg_tax_pre_get_block_templates( $output, $query, $template_type ) {
 	// Do not remove the tax query when querying for a specific slug.
-	if ( 'wp_template' === $template_type && ( is_numeric( $query ) || empty( $query['slug__in'] ) ) ) {
+	if ( 'wp_template' === $template_type && ! empty( $query['slug__in'] ) ) {
 		add_action( 'pre_get_posts', 'gutenberg_remove_tax_query_for_templates' );
 	}
 	return $output;
 }
 
 add_filter( 'get_block_templates', 'gutenberg_tax_get_block_templates', 10, 3 );
-add_action( 'get_block_template', 'gutenberg_tax_get_block_templates', 10, 3 );
 function gutenberg_tax_get_block_templates( $output, $query, $template_type ) {
-	if ( 'wp_template' === $template_type && ( is_numeric( $query ) || empty( $query['slug__in'] ) ) ) {
+	if ( 'wp_template' === $template_type && ! empty( $query['slug__in'] ) ) {
 		remove_action( 'pre_get_posts', 'gutenberg_remove_tax_query_for_templates' );
 	}
 	return $output;
@@ -133,3 +132,19 @@ function gutenberg_get_the_terms( $terms, $object_id, $taxonomy ) {
 	}
 	return $terms;
 }
+
+
+// We need to set the theme for the template when it's created. See:
+// https://github.com/WordPress/wordpress-develop/blob/b2c8d8d2c8754cab5286b06efb4c11e2b6aa92d5/src/wp-includes/rest-api/endpoints/class-wp-rest-templates-controller.php#L571-L578
+function gutenberg_set_active_template_theme( $changes, $request ) {
+	$template = $request['id'] ? get_block_template( $request['id'], 'wp_template' ) : null;
+	if ( $template ) {
+		return $changes;
+	}
+	$changes->tax_input = array(
+		'wp_theme' => isset( $request['theme'] ) ? $request['theme'] : get_stylesheet(),
+	);
+	return $changes;
+}
+
+add_action( 'rest_pre_insert_wp_template', 'gutenberg_set_active_template_theme', 10, 2 );