Putin is addressing his staff about the Kursk invasion.
https://yewtu.be/watch?v=u1qHC_471C8
https://youtube.com/watch?v=u1qHC_471C8
He says that the #1 priority of the Def Ministry is to force out the Ukrainians. But he does not mention the army, only the FSB (Federal Security Service) and the National Guard (Rosgvardiya) - used against the sabotage and recon groups, and some vague combat objectives of the National Guard. Later in the speech he does say that the RuAF doing well in its effort to "liberate" Donetsk and Luhansk, so that is about only the offensive operations of the SMO.
Wyatt of DPA says form open sources it can be gathered that Russians use airplanes, helicopters, and drones heavily, but on the ground it seems it's mostly special forces that engages the AFU on the ground in Kursk. It does seem that regular units of the Russian army aren't there to halt the advances.
So I assume the fight - for now - is the job of the oblast itself, the local units of the National Guard. The federal government complements them with air force, FSB, and other special forces. I wonder why.