Google search api linkage to user session bookmarks?

If this is incorrect group, please let me know and I’ll try elsewhere. thanks for your patience with a newbie to this forum.

This is a query on Why Not, and if there is such an add-on please let me know, I’m yet to find it.

In the early days there were add-ons that hooked into search result feeds to enhance the experience for users, the add-ons would attribute results with useful insight for the user.

What I have been looking for all these years and cannot understand Why there is not a design solution is a way to display somewhere in context to search result a reference to any bookmarks of active user session that belong to same tld, this obviously could then be extended to provide other contextual information based on the common linkage.

Conceptually it seems like a useful thing to have. Can someone help me understand why this is not possible, is it due to google api restrictions/security features to prevent phishing or other scams?

If so, is there another search engine that allows you to code in attribution in this manner? History on the subject would be greatly appreciated so I can stop the painful wanting for such a feature on my browser.