>>/48834/
Yes, they withdrew from Izium to avoid being encircled. But they are in danger of being encircled In Lyman if they are not operationally encircled already. It's probably too late for them to pull out from Lyman now as well, they have allowed this. As the Rybar map >>/48829/ shows, the only remaining road network they have is through Zarichne which is very close to the front now. However, the road leading to the river from Kolodydyazi does actually run-through to a small road over a dam and then to Terny, so that may enable some resupply, but that is at risk as well.
They were planing the referendums for a long time and they had said before these offensives that they were going to happen at about this time. I think the two are unrelated. Remember, any mobilised reserves are not going to reach the front for months anyway and the Russians would have known about the troop build-ups for these offensives and would have an idea of what effect they would have. I think that if they were mobilising due to it they would have done so pre-emptively.
The forces in Khakiv were spread thin and were more of a screen than anything else, so they fell back very quickly and it does not impact the war in anyway. Lyman is different because they are actually fighting a determined resistance and as I mentioned above the Russians are not going to pull out, it's too late for that. They are committed to this.
So then whether Russia actually has lost the initiative and is in trouble or not depends on the events that will unfold in Lyman. For all we know the Russian may be quite happy letting Ukraine throw their forces into a meat grinder and just waiting for the Ukrainians to run out of steam before they counter attack. Conversely, maybe they are in danger, maybe the Ukrainians will take Lyman and then push further east. We don't know.