The Ukrainian push into Kursk appears to be considerably more than "some partisans ranging over the border" - something which had already been happening for a long time before they moved into Kursk with more force.
The forces deployed in Kursk are relatively small and have no chance of accomplishing any major strategic goals, but I'm not sure they fit particularly well with any accepted definitions of "partisans", which typically implies irregular troops, or at least detached light troops, not a corps sized element with armor support.
The attack does coincide with increased rate of terrain losses in eastern Ukraine, so the diversion of manpower and equipment could well be partially responsible for that, but Russian progress in eastern Ukraine was slowly happening even prior to that.
Small and strategically ineffective though it may be (at its most expansive it was a tiny fraction of ground that Russia occupied within Ukraine) it also is a major insult to Russia and I think more intended to give foreign press something to talk about to distract them from losses to Russia elsewhere. If they had timed it right it might have also been a bargaining chip for negotiation, but I think Putin correctly believes he can retake it before any real negotiation takes place.
I doubt the long-term benefit of the Kursk operation, but I'm not sure they had a lot of way better options either. From the outset, the size and military asset disparity made Ukraine's long-term prospects pretty bleak one way or another, external support or not.
Russia's performance in this campaign has been abysmal. The inability to achieve its decapitation strike at the beginning of the attack quickly led into revealing the horrible logistics and lack of communication which cemented its losses during Ukraine's counteroffensive. It failed to ever achieve air superiority, even in early phases of the conflict. It was unable to protect general staff leading to massive losses in leadership. Despite being on a war economy, Russia has shown an inability to replace losses of modern equipment and has resorted to pulling long-outdated equipment out of mothballs to backfill for the absolutely tremendous number of vehicles lost. Morale has been terrible, and the sheer number of on-video suicides of Russian soldiers has been horrific. Discipline has been bad, and if the POW interviews are anything to go by, many Russian soldiers are as afraid of being executed by their officers as they are of being killed by Ukrainians.
Given enough time Russia will absolutely win this war, but they should have won it in a matter of three weeks, or three months, not three years.