There isn’t a filter for ‘assigned’, or ‘not-assigned’ on the Discourse advanced search page. It has been asked for previously though: What is advanced search magic filter to see assigned topics and messages?. Maybe that is something that we should look into again.
If the Data Explorer plugin is installed on your site, we could probably help to come up with a query that would return unassigned topics. The built in “List of assigned topics by user” Data Explorer query would be a good starting point for that query.