Backporting changes from WordPress/gutenberg#46248

src/wp-includes/rest-api/endpoints/class-wp-rest-templates-controller.php

@@ -150,14 +150,21 @@ public function register_routes() {
 	 * Returns the fallback template for the given slug.
 	 *
 	 * @since 6.1.0
+	 * @since 6.3.0 Ignore empty templates.
 	 *
 	 * @param WP_REST_Request $request The request instance.
 	 * @return WP_REST_Response|WP_Error
 	 */
 	public function get_template_fallback( $request ) {
 		$hierarchy         = get_template_hierarchy( $request['slug'], $request['is_custom'], $request['template_prefix'] );
-		$fallback_template = resolve_block_template( $request['slug'], $hierarchy, '' );
-		$response          = $this->prepare_item_for_response( $fallback_template, $request );
+
+		do {
+			$fallback_template = resolve_block_template( $request['slug'], $hierarchy, '' );
+			array_shift( $hierarchy );
+		} while ( ! empty( $hierarchy ) && empty( $fallback_template->content ) );
+
+		$response = $this->prepare_item_for_response( $fallback_template, $request );
+
 		return rest_ensure_response( $response );
 	}
 

tests/phpunit/tests/rest-api/wpRestTemplatesController.php

@@ -837,5 +837,12 @@ public function test_get_template_fallback() {
 		$request->set_param( 'template_prefix', 'page' );
 		$response = rest_get_server()->dispatch( $request );
 		$this->assertSame( 'page', $response->get_data()['slug'], 'Should fallback to `page.html`.' );
+		// Should fallback to `index.html`.
+		$request->set_param( 'slug', 'author' );
+		$request->set_param( 'ignore_empty', true );
+		$request->set_param( 'template_prefix', 'tag' );
+		$request->set_param( 'is_custom', false );
+		$response = rest_get_server()->dispatch( $request );
+		$this->assertSame( 'index', $response->get_data()['slug'], 'Should fallback to `index.html` when  ignore_empty is `true`.' );
 	}
 }