My 2-cents is In the past couple of months, leading up to May 9th, Wagner was pushing ever harder, Putin was getting him more weapons and support so that all of Bahkmut could be taken. In order to prevent that, Ukraine sent reinforcements. However, these reinforcements were NOT part of a counter-offensive, they were simply sent to prevent a full-capture of Bahkmut. Then, when the May 9th date passed Russians stopped their all-out effort to capture Bahkmut. Therefore, the addition of Ukrainians tipped the balance so that it was Ukraine gaining ground. So for me, both commentaries you quoted are correct. The Ukrainians have captured some land. But so far it isn't material.

The question for Ukraine is does it send even more reinforcements to continue their momentum, or lock it off there? My guess is the latter because there's nothing left of Bahkmut to fight over.