The backslash before the single quote in the CONCAT function escapes the single quote. So, it was parsing the query as something else and was throwing the error. By escaping the backslash before the single quote fixed it.
UPDATE `sss_notifications` SET `object_type`=CONCAT('App\\Models\\', object_type) WHERE `object_type` NOT LIKE 'App\\\\Models\\\\%';
I also needed to escape the other backslash after 'App' in the CONCAT function.