Use type=module for <script> tags; may be necessary and should not hurt

CRM/Inlay/Page/Demo.php

 <?php
+
 use CRM_Inlay_ExtensionUtil as E;
 
 class CRM_Inlay_Page_Demo extends CRM_Core_Page {
@@ -27,7 +28,7 @@ class CRM_Inlay_Page_Demo extends CRM_Core_Page {
     $editUrl = str_replace('{id}', $inlay->getID(), $inlay->getInstanceEditURLTemplate());
     $this->assign('editUrl', CRM_Utils_System::url($editUrl));
     $cacheBuster = time();
-    $this->assign('scriptTag', "<script src=\"{$inlay->getBundleUrl()}?nocache=$cacheBuster\" data-inlay-id=\"{$inlay->getPublicID()}\" defer></script>");
+    $this->assign('scriptTag', "<script type=module src=\"{$inlay->getBundleUrl()}?nocache=$cacheBuster\" data-inlay-id=\"{$inlay->getPublicID()}\" ></script>");
 
     parent::run();
   }

Civi/Api4/Action/Inlay/CreateBundle.php

 <?php
+
 namespace Civi\Api4\Action\Inlay;
+
 /**
  * Provides way to update the .js bundles for each inlay.
  */
+
 use CRM_Inlay_ExtensionUtil as E;
 use Civi\Api4\Generic\Result;
 use Civi\Inlay\Config as InlayConfig;
 use Civi\Api4\Generic\Traits\DAOActionTrait;
 use Civi;
+
 /**
  * InlayType.get action
  *
@@ -72,11 +76,10 @@ class CreateBundle extends \Civi\Api4\Generic\AbstractQueryAction {
         $libraryCode
         CiviCRMInlay.app.bundleInfo($now, $publicID);
         $externalScript
-        (function(){
-          var i = window.CiviCRMInlay;
+        ((i) => {
           i.inlays[$publicID] = $initData;
           i.app.bootWhenReady();
-        })();
+        })(window.CiviCRMInlay);
         JAVASCRIPT;
 
       // Get public storage.
@@ -107,5 +110,4 @@ class CreateBundle extends \Civi\Api4\Generic\AbstractQueryAction {
 
     return (array) civicrm_api4($this->getEntityName(), 'get', $params);
   }
-
 }

ang/inlay/Inlays.js

@@ -152,7 +152,7 @@
     }
 
     $scope.getScript = function(i) {
-      var mainScript = encodeToHTML(`<script src="${i.scriptUrl}" data-inlay-id="${i.public_id}" ></script>`);
+      var mainScript = encodeToHTML(`<script type=module src="${i.scriptUrl}" data-inlay-id="${i.public_id}" ></script>`);
       var wpShortcode = encodeToHTML(`[inlay id="${i.public_id}"]`);
       console.log({mainScript, wpShortcode});