I think people are being too pessimistic about Trump in this context. Trump is terrible, sure, but one of the things that makes him terrible is total self-interest. I don’t think he’s as reliable a puppet of Putin as commonly thought.
I’m thinking perhaps Putin is worried Trump might decide to flip the script and act the tough guy against him this time, since Putin is significantly weaker now than in his previous term. Getting Kursk back would be absolutely vital if it looks like Trump is going to try to freeze the conflict or force negotiations.
The GOP as a whole is not reliably pro-Putin either, there are some hawks in there that would love to finish Putin off.
In general, this is an uncertain time approaching.