diff --git a/gulpfile.mjs b/gulpfile.mjs
index c4314bbf3..bf589fbc3 100644
--- a/gulpfile.mjs
+++ b/gulpfile.mjs
@@ -214,7 +214,12 @@ function createWebpackConfig(
     : [
         [
           "@babel/preset-env",
-          { corejs: "3.32.2", shippedProposals: true, useBuiltIns: "usage" },
+          {
+            corejs: "3.32.2",
+            exclude: ["web.structured-clone"],
+            shippedProposals: true,
+            useBuiltIns: "usage",
+          },
         ],
       ];
   const babelPlugins = isModule
diff --git a/src/display/annotation_storage.js b/src/display/annotation_storage.js
index 05d19d804..e2a80b230 100644
--- a/src/display/annotation_storage.js
+++ b/src/display/annotation_storage.js
@@ -20,7 +20,7 @@ import { MurmurHash3_64 } from "../shared/murmurhash3.js";
 const SerializableEmpty = Object.freeze({
   map: null,
   hash: "",
-  transfers: undefined,
+  transfer: undefined,
 });
 
 /**
@@ -181,7 +181,7 @@ class AnnotationStorage {
     }
     const map = new Map(),
       hash = new MurmurHash3_64(),
-      transfers = [];
+      transfer = [];
     const context = Object.create(null);
     let hasBitmap = false;
 
@@ -203,13 +203,13 @@ class AnnotationStorage {
       // during serialization with SVG images.
       for (const value of map.values()) {
         if (value.bitmap) {
-          transfers.push(value.bitmap);
+          transfer.push(value.bitmap);
         }
       }
     }
 
     return map.size > 0
-      ? { map, hash: hash.hexdigest(), transfers }
+      ? { map, hash: hash.hexdigest(), transfer }
       : SerializableEmpty;
   }
 }
@@ -224,17 +224,11 @@ class PrintAnnotationStorage extends AnnotationStorage {
 
   constructor(parent) {
     super();
-    const { map, hash, transfers } = parent.serializable;
+    const { map, hash, transfer } = parent.serializable;
     // Create a *copy* of the data, since Objects are passed by reference in JS.
-    const clone = structuredClone(
-      map,
-      (typeof PDFJSDev === "undefined" ||
-        PDFJSDev.test("SKIP_BABEL || TESTING")) &&
-        transfers
-        ? { transfer: transfers }
-        : null
-    );
-    this.#serializable = { map: clone, hash, transfers };
+    const clone = structuredClone(map, transfer ? { transfer } : null);
+
+    this.#serializable = { map: clone, hash, transfer };
   }
 
   /**
diff --git a/src/display/api.js b/src/display/api.js
index 2d3837b25..e5ed6addb 100644
--- a/src/display/api.js
+++ b/src/display/api.js
@@ -1802,7 +1802,7 @@ class PDFPageProxy {
         '_pumpOperatorList: Expected valid "renderingIntent" argument.'
       );
     }
-    const { map, transfers } = annotationStorageSerializable;
+    const { map, transfer } = annotationStorageSerializable;
 
     const readableStream = this._transport.messageHandler.sendWithStream(
       "GetOperatorList",
@@ -1812,7 +1812,7 @@ class PDFPageProxy {
         cacheKey,
         annotationStorage: map,
       },
-      transfers
+      transfer
     );
     const reader = readableStream.getReader();
 
@@ -1942,14 +1942,7 @@ class LoopbackPort {
 
   postMessage(obj, transfer) {
     const event = {
-      data: structuredClone(
-        obj,
-        (typeof PDFJSDev === "undefined" ||
-          PDFJSDev.test("SKIP_BABEL || TESTING")) &&
-          transfer
-          ? { transfer }
-          : null
-      ),
+      data: structuredClone(obj, transfer ? { transfer } : null),
     };
 
     this.#deferred.then(() => {
@@ -2853,7 +2846,7 @@ class WorkerTransport {
           "please use the getData-method instead."
       );
     }
-    const { map, transfers } = this.annotationStorage.serializable;
+    const { map, transfer } = this.annotationStorage.serializable;
 
     return this.messageHandler
       .sendWithPromise(
@@ -2864,7 +2857,7 @@ class WorkerTransport {
           annotationStorage: map,
           filename: this._fullReader?.filename ?? null,
         },
-        transfers
+        transfer
       )
       .finally(() => {
         this.annotationStorage.resetModified();