IMHO it's a ER request and I remember I've asked for this before as there doesn't seem to be a related object we can link to so I guess the product itself doesn't it a more "internal" way with SQL query rather than what we can get at through related objects in QueryTool.
It also seems a little strange that you also can't search for "nothing" in the search bar (null) and return all the results that you have access to see. Like an asterisk or percentage symbol
Sounds like it might be a combination of a SQL view and some LDSD query criteria
There is currently no way to create a query in such way that it will only show you articles that you have access to.
What you can do is either have a query that lists all articles and add a filter as prompt to search by a Knowledge Domains.
OR you could make a separate query for each Knowledge Domain, and publish it to each group that has access to said domain.
I understand that this is not the answer you were looking for, but I encourage you to log Enhancement Request which can be considered for future releases of Service Desk based on number of votes and the impact it has on our customers.
Enhancement Requests page: