I don't think so. Adding Kharkov region will require Russia to reasonably control a large part of it, not a small piece on the northeastern border. I think Ukraine has another 12-24 months before Russia will try to claim another region.
I think alot of that may depend on Ukraine ability to effectively reform a effective defensive line here. They absolutely do have the forces to fight effectively so, it's more they don't seem to be willing to make that decision to pullback far enough also to a not insignificant degree were? Drone ranges have indeed expanded and actually building effective defence positions require a earlier commitment then they did previously.
Im also guessing moral is still a growing issue. And imop the critical factor as I believe it's likely to break before the army itself does. Tho I do do try not to make a prediction on it I don't discard it as a real potential either.
I 100% agree the Ukrainian army is still a potent and effective force, but it's also never really been a truly cohesive force a factor that does not help with these issues.
Add in what control the top command does have appears to be a stubborn insistence on holding territory and political considerations over tactical or strategic ones. Something that has itself become a moral issue and I think despite the probloms the Russian army itself has there is a real threat of a breakthrough snowballing into a partial if not significant collapse somewhere along the front.
Especially in the areas mostly manned by understaffed and under equipped territorial defence brigades. they have shown a small but increasing breakdown in discipline in the last year there is a real risk of a unplanned retreat or a rout. And currently there is not alot of options for plugging holes. In short Russia may make that claim not due to the totality of occupation but on the speed of it. In such a case the added demand may increase pressure to accept such a deal.
Kharkov region also may not be the claim as much as it makes sence for Russia Dnipropetrovsk Oblast may also be a option if the current pace of operations continues. Or at least the parts east of the dinipr river. It's also Ukraines most important industrial region. Added to that is at least for now the lack of prepared defences compared to other directions and in general it's topography and i wouldn't be surprised to see it as a region Russia continues to push into. I don't think Ukraine has the forces to cut them off and it would also make logistics north to south a real headache. They also currently have a degree of momentum in the region. Granted I don't think they could occupy it in any reasonable length of time, but they could threaten it enough to bring Ukraine to the table