I just played a Warzone Turbo match in which I was awarded two kills for the Warden. However, these did not get added to my Warden kill commendation, which has been frozen at 4/7 for quite some time. I recall the same issue with Warzone Firefight, which I figured to be a singular issue with the beta.
This is not an issue with the game or beta.
The only way to make your warden commendation count is to get the last shot on the warden (be the one to actually kill it)
Many people get the boss takedown message when the warden dies. This is not the same thing as killing the warden.