Index: src/wp-admin/css/edit.css
===================================================================
--- src/wp-admin/css/edit.css	(revision 54156)
+++ src/wp-admin/css/edit.css	(working copy)
@@ -725,6 +725,17 @@
 	padding-left: 0;
 }
 
+/* Better position for the WordPress admin notices. */
+.privacy-settings .notice,
+.site-health .notice {
+	margin: 25px 20px 15px 22px;
+}
+
+.privacy-settings .notice ~ .notice,
+.site-health .notice ~ .notice {
+	margin-top: 5px;
+}
+
 /* Emulates .wrap h1 styling */
 .privacy-settings-header h1,
 .health-check-header h1 {
Index: src/wp-admin/css/site-health.css
===================================================================
--- src/wp-admin/css/site-health.css	(revision 54156)
+++ src/wp-admin/css/site-health.css	(working copy)
@@ -284,17 +284,6 @@
 	padding-left: 20px;
 }
 
-
-/* Better position for the WordPress admin notices and update nag. */
-.site-health .notice {
-	margin: 5px 20px 15px 22px;
-}
-
-.site-health .update-nag {
-	margin-bottom: 20px;
-	margin-left: 22px;
-}
-
 .health-check-wp-paths-sizes.spinner {
 	visibility: visible;
 	float: none;