Embed header or Discourse as Header provider

I have a site (not Wordpress) and a forum. I customized my site to use Discourse as an SSO provider to register/authorize/sync users on both.

I want to integrate the site and forum more tightly.
First, I want to use Discourse as Notification and Private Messages provider. So, I’ve migrated all users notifications and PMs into Discourse. But there is a problem. Right now I should forward users to Discourse forum to view, mark as read, delete, etc. notifications/PMs.

Long time I saw only one solution: to embed notification and PMs dropdowns on my site and interact with Discourse API via fetch. It will be hard and seems a lot of coding. But wait! I got a new idea! I can have the Discourse header on the site, it will resolve the problem, but how to embed Discourse header to be able to interact with it? Any tips?