If you haven't already, please see the Cookieless Embedding Guide for a high-level overview of cookieless embedding and how it's supposed to work. Most cookieless embed issues are resolved by the following:
For Looker users and developers, the challenge of creating a truly integrated, multi-tabbed dashboard experience in Looker has long been a point of focus. This post details the progression from manual workarounds to a sophisticated, native solution leveraging the Looker Extension Framework. With an easy-to-install extension, anyone can create a multi-tabbed dashboard experience in Looker, either in a presentation-style format or ad hoc using folders and boards.
See the documentation and the repository