Make the body not scrollable and make a scrollable container div to host #extension-settings.

chrome/browser/resources/extensions/extensions.css

 /* Copyright (c) 2012 The Chromium Authors. All rights reserved.
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file. */
 
+html,
+body {
+  height: 100%;
+  overflow: hidden;
+}
+
 html.loading * {
   -webkit-transition-duration: 0 !important;
 }
 
 html:not(.focus-outline-visible)
 :enabled:focus:-webkit-any(input[type='checkbox'], input[type='radio']) {
   /* Cancel border-color for :focus specified in widgets.css. */
   border-color: rgba(0, 0, 0, 0.25);
 }
 
@@ skipping 68 matching lines @@
 }
 
 #extension-settings #page-header {
   /* These values match the .page values. */
   -webkit-margin-end: 24px;
   min-width: 576px;
 }
 
 /* Contents */
 
+#page-container {
+  height: 100%;
+  overflow-y: auto;
+}
+
 #extension-settings {
   max-width: 738px;
 }
 
 #no-extensions-message {
   font-weight: bold;
 }
 
 #suggest-gallery {
   -webkit-padding-start: 10px;
@@ skipping 230 matching lines @@
 /* Sideload Wipeout */
 
 .sideload-wipeout-learn-more {
   text-decoration: none;
 }
 
 .sideload-wipeout-banner .page-banner-text {
   -webkit-padding-start: 8px;
   background-image: none;
 }