I made all the adjustments in the blomstra search extension, not in this bookmark extension.
So to have said it, I am not a Laravel / Flarum pro. But my customizations are in such a way that I have written a function which gets the bookmarked posts of the user from the database.
And I have changed the data function so that it simply checks if the request is filtering by "is:bookmarked", so $filter_bookmarked is set to true and this filter is removed from the request (cleaned up).
This way the bookmarked discussions from the user are fetched (via my new function) and then two filters (type & rawId) are added to the blomstra search query.
However, I have not really tested this intensively. For example, if I enter something in the search and want to see the search results only from the bookmarked discussions, i only get discussions which have a hit in the title (and no discussions which have a hint in the posts). I assume this is because I filter for discussions and posts are ignored...
But at least it shows the bookmarks.