I always though the opposite. In my mind going to smaller ice with less room to figure out passing/skating lanes benefited d-man more and was harder for offensive players to overcome. But I thought that when I though they all played olympic size ice, which someone said is not the case anymore? So I don't know.
KHL ice is mostly(maybe all?) NHL size, I believe.
The problem for defenseman is that their defending angles all change when rink size change and defender errors are more serious than defenseman errors.
Also, systems and interaction with partner are more important for a defenseman.
A forward can screw things up all game and not have anything seriously bad happen, then they score 1 goal and they end up being helpful. It’s harder for a defenseman to screw up all game and not have something seriously bad happen and harder for them to have an offensive play that makes their day.
So generally it’s harder to add a defenseman last minute than a forward for the reasons above, imo. I believe teams actually find that to be true even with NHL players acquired at the deadline, easier for forwards to integrate into the new team.