diff --git src/wp-admin/edit-form-blocks.php src/wp-admin/edit-form-blocks.php
index 0268bc8ae8..79e8e5e919 100644
--- src/wp-admin/edit-form-blocks.php
+++ src/wp-admin/edit-form-blocks.php
@@ -32,14 +32,6 @@ $current_screen->is_block_editor( true );
 _load_remote_block_patterns();
 _load_remote_featured_patterns();
 
-// Default to is-fullscreen-mode to avoid jumps in the UI.
-add_filter(
-	'admin_body_class',
-	static function( $classes ) {
-		return "$classes is-fullscreen-mode";
-	}
-);
-
 /*
  * Emoji replacement is disabled for now, until it plays nicely with React.
  */
diff --git src/wp-admin/includes/admin-filters.php src/wp-admin/includes/admin-filters.php
index d03881c8ac..23e4a1163b 100644
--- src/wp-admin/includes/admin-filters.php
+++ src/wp-admin/includes/admin-filters.php
@@ -47,6 +47,10 @@ add_action( 'admin_head', 'wp_site_icon' );
 add_action( 'admin_head', 'wp_admin_viewport_meta' );
 add_action( 'customize_controls_head', 'wp_admin_viewport_meta' );
 
+// Body classes for admin pages.
+add_filter( 'admin_body_class', 'body_class_edit_form_blocks' );
+add_filter( 'admin_body_class', 'body_class_options_privacy' );
+
 // Prerendering.
 if ( ! is_customize_preview() ) {
 	add_filter( 'admin_print_styles', 'wp_resource_hints', 1 );
diff --git src/wp-admin/includes/misc.php src/wp-admin/includes/misc.php
index f8cf82acf7..b8b1c22837 100644
--- src/wp-admin/includes/misc.php
+++ src/wp-admin/includes/misc.php
@@ -1571,3 +1571,36 @@ function wp_check_php_version() {
 
 	return $response;
 }
+
+/**
+ * Adds 'is-fullscreen-mode' body class in Block Editor screens to
+ * avoid jumps in the UI.
+ *
+ * @param string $classes Space-separated list of CSS classes.
+ * @return string $classes String of classes.
+ */
+function body_class_edit_form_blocks( $classes ) {
+	$current_screen = get_current_screen();
+
+	if ( ! is_null( $current_screen->id ) && in_array( $current_screen->id, array( 'post', 'page' ) ) ) {
+		$classes .= ' is-fullscreen-mode';
+	}
+
+	return $classes;
+}
+
+/**
+ * Adds 'options-privacy' in Privacy Options page.
+ *
+ * @param string $classes Space-separated list of CSS classes.
+ * @return string $classes String of classes.
+ */
+function body_class_options_privacy( $classes ) {
+	$current_screen = get_current_screen();
+
+	if ( ! is_null( $current_screen->id ) && 'options-privacy' === $current_screen->id ) {
+		$classes .= ' privacy-settings';
+	}
+
+	return $classes;
+}
diff --git src/wp-admin/options-privacy.php src/wp-admin/options-privacy.php
index fbd69f23a7..08bdc95340 100644
--- src/wp-admin/options-privacy.php
+++ src/wp-admin/options-privacy.php
@@ -18,15 +18,6 @@ if ( isset( $_GET['tab'] ) && 'policyguide' === $_GET['tab'] ) {
 	return;
 }
 
-add_filter(
-	'admin_body_class',
-	static function( $body_class ) {
-		$body_class .= ' privacy-settings ';
-
-		return $body_class;
-	}
-);
-
 $action = isset( $_POST['action'] ) ? $_POST['action'] : '';
 
 get_current_screen()->add_help_tab(
diff --git src/wp-admin/privacy-policy-guide.php src/wp-admin/privacy-policy-guide.php
index 6581bb412a..69055b1193 100644
--- src/wp-admin/privacy-policy-guide.php
+++ src/wp-admin/privacy-policy-guide.php
@@ -17,15 +17,6 @@ if ( ! class_exists( 'WP_Privacy_Policy_Content' ) ) {
 	include_once ABSPATH . 'wp-admin/includes/class-wp-privacy-policy-content.php';
 }
 
-add_filter(
-	'admin_body_class',
-	static function( $body_class ) {
-		$body_class .= ' privacy-settings ';
-
-		return $body_class;
-	}
-);
-
 wp_enqueue_script( 'privacy-tools' );
 
 require_once ABSPATH . 'wp-admin/admin-header.php';
diff --git src/wp-includes/sitemaps/class-wp-sitemaps-renderer.php src/wp-includes/sitemaps/class-wp-sitemaps-renderer.php
index 0069b11126..0bc607e26b 100644
--- src/wp-includes/sitemaps/class-wp-sitemaps-renderer.php
+++ src/wp-includes/sitemaps/class-wp-sitemaps-renderer.php
@@ -251,12 +251,7 @@ class WP_Sitemaps_Renderer {
 	 */
 	private function check_for_simple_xml_availability() {
 		if ( ! class_exists( 'SimpleXMLElement' ) ) {
-			add_filter(
-				'wp_die_handler',
-				static function () {
-					return '_xml_wp_die_handler';
-				}
-			);
+			add_filter( 'wp_die_handler', array( __CLASS__, 'return_xml_wp_die_handler' ) );
 
 			wp_die(
 				sprintf(
@@ -271,4 +266,15 @@ class WP_Sitemaps_Renderer {
 			);
 		}
 	}
+
+	/**
+	 * Returns the _xml_wp_die_handler function name.
+	 *
+	 * Used to prevent using a lambda function in the 'wp_die_handler' filter.
+	 *
+	 * @return string The XML WP Die handler function name.
+	 */
+	protected static function return_xml_wp_die_handler() {
+		return '_xml_wp_die_handler';
+	}
 }
diff --git src/wp-includes/theme.php src/wp-includes/theme.php
index ed24f677ef..acb6ae92a6 100644
--- src/wp-includes/theme.php
+++ src/wp-includes/theme.php
@@ -1996,19 +1996,18 @@ function wp_update_custom_css_post( $css, $args = array() ) {
 	 * Filters the `css` (`post_content`) and `preprocessed` (`post_content_filtered`) args
 	 * for a `custom_css` post being updated.
 	 *
-	 * This filter can be used by plugin that offer CSS pre-processors, to store the original
+	 * This filter can be used by plugins that offer CSS pre-processors to store the original
 	 * pre-processed CSS in `post_content_filtered` and then store processed CSS in `post_content`.
-	 * When used in this way, the `post_content_filtered` should be supplied as the setting value
-	 * instead of `post_content` via a the `customize_value_custom_css` filter, for example:
 	 *
 	 * <code>
-	 * add_filter( 'customize_value_custom_css', function( $value, $setting ) {
-	 *     $post = wp_get_custom_css_post( $setting->stylesheet );
-	 *     if ( $post && ! empty( $post->post_content_filtered ) ) {
-	 *         $css = $post->post_content_filtered;
+	 * add_filter( 'update_custom_css_data', 'my_update_custom_css_data', '10, 2 );
+	 * function my_update_custom_css_data( $data, $args ) {
+	 *     $css_post = wp_get_custom_css_post( $args['stylesheet'] );
+	 *     if ( $css_post && ! empty( $css_post->post_content_filtered ) ) {
+	 *         $data['post_content_filtered'] = $css_post->post_content_filtered;
 	 *     }
-	 *     return $css;
-	 * }, 10, 2 );
+	 *     return $data;
+	 * }
 	 * </code>
 	 *
 	 * @since 4.7.0
