I was basically envisioning it as a "simultaneous search"
It's kind of like a custom lens, where Kagi would only return results that I have bookmarked in Diigo. Except, it would always show the first 5 results in a small box on the right side of the normal Kagi results.
In terms of how it would work:
Whenever I would do a keyword search, the widget would simultaneously do a search of my Diigo library. If there were any results returned by the Diigo search, it would display them in a small box either within the Kagi search results or off to the side.
For reference, Diigo API: https://www.diigo.com/api_dev
Of course, (while I would probably build this for fun), this example is primarily just to suggest that a use case for custom widgets is "simultaneously search another website and include those results"
But, building off of https://kagifeedback.org/d/1560-bookmarks, it could also be really interesting to hook into other websites/services (Diigo, Instapaper, Memex, Wallabag) as a "bookmarks provider".