diff --git a/core/lib/Drupal/Core/Theme/ThemeInitialization.php b/core/lib/Drupal/Core/Theme/ThemeInitialization.php
index 34b95e955c77560ef163d75a9469301d8de04b72..c81be077f54cec969e432ce82332f5275cf752c2 100644
--- a/core/lib/Drupal/Core/Theme/ThemeInitialization.php
+++ b/core/lib/Drupal/Core/Theme/ThemeInitialization.php
@@ -140,11 +140,18 @@ public function loadActiveTheme(ActiveTheme $active_theme) {
       include_once $this->root . '/' . $active_theme->getOwner();
 
       if (function_exists($theme_engine . '_init')) {
+        @trigger_error('THEME_ENGINE_init() is deprecated in drupal:9.3.0 and removed in drupal:10.0.0. There is no replacement. See https://www.drupal.org/node/3246978', E_USER_DEPRECATED);
         foreach ($active_theme->getBaseThemeExtensions() as $base) {
           call_user_func($theme_engine . '_init', $base);
         }
         call_user_func($theme_engine . '_init', $active_theme->getExtension());
       }
+      else {
+        foreach ($active_theme->getBaseThemeExtensions() as $base) {
+          $base->load();
+        }
+        $active_theme->getExtension()->load();
+      }
     }
     else {
       // include non-engine theme files
diff --git a/core/modules/system/tests/src/Functional/Theme/EngineNyanCatTest.php b/core/modules/system/tests/src/Functional/Theme/EngineNyanCatTest.php
index 7a227da1ddb225458271b24bc7cd091b0f73f4fe..0b8269a2cd3199865a6d76130babaf9dac7e3552 100644
--- a/core/modules/system/tests/src/Functional/Theme/EngineNyanCatTest.php
+++ b/core/modules/system/tests/src/Functional/Theme/EngineNyanCatTest.php
@@ -30,8 +30,15 @@ protected function setUp(): void {
 
   /**
    * Ensures a theme's template is overridable based on the 'template' filename.
+   *
+   * @group legacy
+   *
+   * @todo https://www.drupal.org/project/drupal/issues/3246981 Remove
+   *   nyan_cat_init() and the legacy group and expected deprecation from this
+   *   test.
    */
   public function testTemplateOverride() {
+    $this->expectDeprecation('THEME_ENGINE_init() is deprecated in drupal:9.3.0 and removed in drupal:10.0.0. There is no replacement. See https://www.drupal.org/node/3246978');
     $this->config('system.theme')
       ->set('default', 'test_theme_nyan_cat_engine')
       ->save();
diff --git a/core/themes/engines/twig/twig.engine b/core/themes/engines/twig/twig.engine
index 759fafcfb70158bff3468b2b595bebe27126ef0a..bcc984a02e24546387d857dd9ae38acd1d52f1d0 100644
--- a/core/themes/engines/twig/twig.engine
+++ b/core/themes/engines/twig/twig.engine
@@ -26,16 +26,6 @@ function twig_extension() {
   return '.html.twig';
 }
 
-/**
- * Includes .theme file from themes.
- *
- * @param \Drupal\Core\Extension\Extension $theme
- *   The theme extension object.
- */
-function twig_init(Extension $theme) {
-  $theme->load();
-}
-
 /**
  * Implements hook_render_template().
  *