diff --git a/src/wp-includes/block-template-utils.php b/src/wp-includes/block-template-utils.php
index 6a53fd6730..28efb5cbad 100644
--- a/src/wp-includes/block-template-utils.php
+++ b/src/wp-includes/block-template-utils.php
@@ -913,7 +913,7 @@ function block_footer_area() {
  */
 function wp_generate_block_templates_export_file() {
 	if ( ! class_exists( 'ZipArchive' ) ) {
-		return new WP_Error( __( 'Zip Export not supported.' ) );
+		return new WP_Error( 'missing_zip_package', __( 'Zip Export not supported.' ) );
 	}
 
 	$obscura  = wp_generate_password( 12, false, false );
@@ -921,7 +921,7 @@ function wp_generate_block_templates_export_file() {
 
 	$zip = new ZipArchive();
 	if ( true !== $zip->open( $filename, ZipArchive::CREATE ) ) {
-		return new WP_Error( __( 'Unable to open export file (archive) for writing.' ) );
+		return new WP_Error( 'unable_to_create_zip', __( 'Unable to open export file (archive) for writing.' ) );
 	}
 
 	$zip->addEmptyDir( 'theme' );
diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-edit-site-export-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-edit-site-export-controller.php
index 1bd40cd637..d5abfa5682 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-edit-site-export-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-edit-site-export-controller.php
@@ -54,8 +54,8 @@ class WP_REST_Edit_Site_Export_Controller extends WP_REST_Controller {
 	 */
 	public function permissions_check() {
 		if ( ! current_user_can( 'edit_theme_options' ) ) {
-			new WP_Error(
-				'rest_cannot_view_url_details',
+			return new WP_Error(
+				'rest_cannot_export_templates',
 				__( 'Sorry, you are not allowed to export templates and template parts.' ),
 				array( 'status' => rest_authorization_required_code() )
 			);
diff --git a/tests/phpunit/tests/rest-api/wpRestEditSiteExportController.php b/tests/phpunit/tests/rest-api/wpRestEditSiteExportController.php
new file mode 100644
index 0000000000..4683d68fed
--- /dev/null
+++ b/tests/phpunit/tests/rest-api/wpRestEditSiteExportController.php
@@ -0,0 +1,156 @@
+<?php
+/**
+ * WP_REST_Edit_Site_Export_Controller tests.
+ *
+ * @package WordPress
+ * @subpackage REST_API
+ * @since 5.9.0
+ */
+
+/**
+ * Tests for WP_REST_Edit_Site_Export_Controller.
+ *
+ * @since 5.9.0
+ *
+ * @covers WP_REST_Edit_Site_Export_Controller
+ *
+ * @group restapi
+ */
+class Tests_REST_WpRestEditSiteExportController extends WP_Test_REST_Controller_Testcase {
+
+	/**
+	 * The REST API route for the edit site export.
+	 *
+	 * @since 5.9.0
+	 *
+	 * @var string
+	 */
+	const REQUEST_ROUTE = '/wp-block-editor/v1/export';
+
+	/**
+	 * Subscriber user ID.
+	 *
+	 * @since 5.9.0
+	 *
+	 * @var int
+	 */
+	protected static $subscriber_id;
+
+	/**
+	 * Set up class test fixtures.
+	 *
+	 * @since 5.9.0
+	 *
+	 * @param WP_UnitTest_Factory $factory WordPress unit test factory.
+	 */
+	public static function wpSetUpBeforeClass( WP_UnitTest_Factory $factory ) {
+		self::$subscriber_id = $factory->user->create(
+			array(
+				'role' => 'subscriber',
+			)
+		);
+	}
+
+	/**
+	 * Delete test data after our tests run.
+	 *
+	 * @since 5.9.0
+	 */
+	public static function wpTearDownAfterClass() {
+		self::delete_user( self::$subscriber_id );
+	}
+
+	/**
+	 * @covers WP_REST_Edit_Site_Export_Controller::register_routes
+	 * @ticket 54448
+	 */
+	public function test_register_routes() {
+		$routes = rest_get_server()->get_routes();
+		$this->assertArrayHasKey( static::REQUEST_ROUTE, $routes );
+		$this->assertCount( 1, $routes[ static::REQUEST_ROUTE ] );
+	}
+
+	/**
+	 * @covers WP_REST_Edit_Site_Export_Controller::permissions_check
+	 *
+	 * @ticket 54448
+	 */
+	public function test_export_for_no_user_permissions() {
+		wp_set_current_user( 0 );
+
+		$request  = new WP_REST_Request( 'GET', static::REQUEST_ROUTE );
+		$response = rest_get_server()->dispatch( $request );
+
+		$this->assertErrorResponse( 'rest_cannot_export_templates', $response, 401 );
+	}
+
+	/**
+	 * @covers WP_REST_Edit_Site_Export_Controller::permissions_check
+	 *
+	 * @ticket 54448
+	 */
+	public function test_export_for_user_with_insufficient_permissions() {
+		wp_set_current_user( self::$subscriber_id );
+
+		$request  = new WP_REST_Request( 'GET', static::REQUEST_ROUTE );
+		$response = rest_get_server()->dispatch( $request );
+
+		$this->assertErrorResponse( 'rest_cannot_export_templates', $response, 403 );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_context_param() {
+		$this->markTestSkipped( 'Controller does not implement context_param().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_get_item() {
+		$this->markTestSkipped( 'Controller does not implement get_item().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_get_items() {
+		$this->markTestSkipped( 'Controller does not implement get_items().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_create_item() {
+		$this->markTestSkipped( 'Controller does not implement create_item().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_update_item() {
+		$this->markTestSkipped( 'Controller does not implement update_item().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_delete_item() {
+		$this->markTestSkipped( 'Controller does not implement delete_item().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_prepare_item() {
+		$this->markTestSkipped( 'Controller does not implement prepare_item().' );
+	}
+
+	/**
+	 * @ticket 54448
+	 */
+	public function test_get_item_schema() {
+		$this->markTestSkipped( 'Controller does not implement get_item_schema().' );
+	}
+}