Log search syntax does works. I use it all the time. Not sure how you passing the syntax. Is it possible for you to share screen shots of the search. Would be easier for me to understand how you searching?
I just did some tests and the user_name log query does work for me, under the same format that you used, so I believe there might be something else at play here.
Are you getting the same result if searching a different user_name by any chance? I do suspect that the issue could be that there are no logs of users that match your search within our 30 days log retention period. If you login with a user and then perform the same log search for their user_name, does that show up for you?
I’m glad the issue has now been resolved for you; if you would like to submit Feedback on this matter, it would be greatly appreciated. Other users can vote on this idea and if it brings enough interest, our Product team that watches over all feedbacks can further send this to our teams and possibly push the update faster.