diff --git a/wp-admin/includes/class-wp-upgrader.php b/wp-admin/includes/class-wp-upgrader.php
index 225a7d4c69..d4db2b082d 100644
--- a/wp-admin/includes/class-wp-upgrader.php
+++ b/wp-admin/includes/class-wp-upgrader.php
@@ -150,8 +150,9 @@ class WP_Upgrader {
 	 * @since 5.9.0
 	 */
 	protected function schedule_temp_backup_cleanup() {
-		wp_schedule_event( time(), 'weekly', 'delete_temp_updater_backups' );
-		add_action( 'delete_temp_updater_backups', array( $this, 'delete_all_temp_backups' ) );
+		if ( false === wp_next_scheduled( 'wp_delete_temp_updater_backups' ) ) {
+			wp_schedule_event( time(), 'weekly', 'wp_delete_temp_updater_backups' );
+		}
 	}
 
 	/**
@@ -1107,51 +1108,6 @@ class WP_Upgrader {
 			true
 		);
 	}
-
-	/**
-	 * Deletes all contents of the temp-backup directory.
-	 *
-	 * @since 5.9.0
-	 *
-	 * @global WP_Filesystem_Base $wp_filesystem WordPress filesystem subclass.
-	 */
-	public function delete_all_temp_backups() {
-		/*
-		 * Check if there's a lock, or if currently performing an Ajax request,
-		 * in which case there's a chance we're doing an update.
-		 * Reschedule for an hour from now and exit early.
-		 */
-		if ( get_option( 'core_updater.lock' ) || get_option( 'auto_updater.lock' ) || wp_doing_ajax() ) {
-			wp_schedule_single_event( time() + HOUR_IN_SECONDS, 'delete_temp_updater_backups' );
-			return;
-		}
-
-		add_action(
-			'shutdown',
-			/*
-			 * This action runs on shutdown to make sure there's no plugin updates currently running.
-			 * Using a closure in this case is OK since the action can be removed by removing the parent hook.
-			 */
-			function() {
-				global $wp_filesystem;
-
-				if ( ! $wp_filesystem ) {
-					include_once ABSPATH . '/wp-admin/includes/file.php';
-					WP_Filesystem();
-				}
-
-				$dirlist = $wp_filesystem->dirlist( $wp_filesystem->wp_content_dir() . 'upgrade/temp-backup/' );
-
-				foreach ( array_keys( $dirlist ) as $dir ) {
-					if ( '.' === $dir || '..' === $dir ) {
-						continue;
-					}
-
-					$wp_filesystem->delete( $wp_filesystem->wp_content_dir() . 'upgrade/temp-backup/' . $dir, true );
-				}
-			}
-		);
-	}
 }
 
 /** Plugin_Upgrader class */
diff --git a/wp-includes/update.php b/wp-includes/update.php
index 42ae3ecf3a..e17c38d0ce 100644
--- a/wp-includes/update.php
+++ b/wp-includes/update.php
@@ -956,6 +956,51 @@ function wp_clean_update_cache() {
 	delete_site_transient( 'update_core' );
 }
 
+/**
+ * Deletes all contents of the temp-backup directory.
+ *
+ * @since 5.9.0
+ *
+ * @global WP_Filesystem_Base $wp_filesystem WordPress filesystem subclass.
+ */
+function wp_delete_all_temp_backups() {
+	/*
+	 * Check if there's a lock, or if currently performing an Ajax request,
+	 * in which case there's a chance we're doing an update.
+	 * Reschedule for an hour from now and exit early.
+	 */
+	if ( get_option( 'core_updater.lock' ) || get_option( 'auto_updater.lock' ) || wp_doing_ajax() ) {
+		wp_schedule_single_event( time() + HOUR_IN_SECONDS, 'wp_delete_temp_updater_backups' );
+		return;
+	}
+
+	add_action(
+		'shutdown',
+		/*
+		 * This action runs on shutdown to make sure there's no plugin updates currently running.
+		 * Using a closure in this case is OK since the action can be removed by removing the parent hook.
+		 */
+		function() {
+			global $wp_filesystem;
+
+			if ( ! $wp_filesystem ) {
+				include_once ABSPATH . '/wp-admin/includes/file.php';
+				WP_Filesystem();
+			}
+
+			$dirlist = $wp_filesystem->dirlist( $wp_filesystem->wp_content_dir() . 'upgrade/temp-backup/' );
+
+			foreach ( array_keys( $dirlist ) as $dir ) {
+				if ( '.' === $dir || '..' === $dir ) {
+					continue;
+				}
+
+				$wp_filesystem->delete( $wp_filesystem->wp_content_dir() . 'upgrade/temp-backup/' . $dir, true );
+			}
+		}
+	);
+}
+
 if ( ( ! is_main_site() && ! is_network_admin() ) || wp_doing_ajax() ) {
 	return;
 }
@@ -980,3 +1025,5 @@ add_action( 'update_option_WPLANG', 'wp_clean_update_cache', 10, 0 );
 add_action( 'wp_maybe_auto_update', 'wp_maybe_auto_update' );
 
 add_action( 'init', 'wp_schedule_update_checks' );
+
+add_action( 'wp_delete_temp_updater_backups', 'wp_delete_all_temp_backups' );
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 40af19f916..701c43afed 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -16,7 +16,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '5.9-alpha-52191';
+$wp_version = '5.9-alpha-52192';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.