The major problem with the water supply is that you stand at the source of some of the sources that feed the Auspiya and Lozva rivers. Above there are bare hills and you cannot see a stream. Considering the current temperatures, the thaw will only begin in March, so only then will you have access to sufficient water. To get ready water, you will have to descend to a much lower altitude and break the ice. They must have known that after walking 1 km from the tent on bare ground and entering the forest, there would be no chance of melt water for another 500 meters. There was no reason to go down to the forest to clean up or get water, and there was no canteen or other equipment to carry water. If the decision to spend a night without fire on the summit had been planned in advance, we would probably have witnessed his notes on the last pages of the diaries. A blizzard that suddenly came towards the end of a late start of the hike, not being able to determine how far the forest was due to poor visibility, and the fear of losing the altitude gained and not being able to set up the tent in the dark...
If there is no possibility of progress due to the blizzard and there is very little time left until dark, setting up camp where you are seems like a logical option.
I remember reading statements that there was a log in the stove or enough pieces of wood to fill the stove. This corresponds to a heating source that will melt the snow to provide enough water for everyone on an extremely cold night and will last 2-3 hours for the tent occupants.
You don't have to go down to the forest and leave to get wood and water.