Drones are just too slow to be easily intercepted by a swept wing jet powered aircraft like the Yak-130.
The whole point of using the Yak-52, like Ukraine is doing, is that it can fly slower, and uses cheaper cannon or machine gun ammunition. The Yak-130 won't be able to stay on target easily, you will need to zoom in and out and it will be hard to target a small slow and low flying target with it. If you start using guided air to air missiles then the cost equation goes out of the window. An R-73 is way more expensive than most drones.
Maybe for the larger Ukrainian drones. But it neither cost effective nor viable against smaller ones.
Russia right now lacks its own serial production of propeller driven aircraft. So the whole idea is a non-starter.
The drones that are being used against Russia and mainly against the Russian interior fly at speeds of 90-180 km/h, I don't think they are slow enough for the Yak-130, with the ability to intercept low-altitude aerial targets in low rated speeds, the aircraft is an alternative solution that may be promising.
The idea of light attack aircraft against UAVs seems like a much less costly solution than using fighters to perform the same function, even if it is to use the R-73 or any other missile, as it would be freeing the Su-30SM and other aircraft capable of more important tasks, saving useful life and preserving the fuselage and reducing maintenance requirements for these aircraft, which reduces the expenses necessary to cover these operations. It's a win-win.
The Yak-130 is sadly being neglected. For example, the Yak-130 could be the lead aircraft from which the UAV/UCAVs will be controlled. The co-pilot of the attack aircraft can take control of UAVs of the Orion and Okhotnik types, which will carry out reconnaissance, provide target designation, carry out air strikes and adjust missile and artillery fire.
The Yak-130 already has a helmet-mounted targeting system and a dual GPS/GLONASS receiver upgrading an inertial reference system for highly accurate navigation and precision targeting, it could still have multiple targeting pods, reconnaissance pods, EW pods and wingtip mounts for budget or other anti-aircraft missiles.
The Su-25 could carry multiple S-5, S-8, S-13 and also S-24 rocket pods ready to support ground troops, while the Yak-130 could carry standoff munitions, 9K121 Vikhr, Kh-25 (several including anti-radial) and Hermes, the latter being ideal. There could also be some Yak-130s with EW pods and reconnaissance pods, and some armed with just anti-aircraft missiles to protect the aircraft, so in theory the Yak-130 fires stand off munitions eliminating any threat to the Su-25 and, seconds then, the Su-25 descends to launch the barrage of rockets and strafe with its cannons.
Using the Yak-130 option in this way would free up the Su-25 or other aircraft for this role, so if, for example, Russia normally sent 4 Su-25s on a mission and two of the Su-25s carried standoff munitions while the others two carried rocket pods or if all four were armed with a mix of each, then using Yak-130's you would release two Su-25's, or in the case of 4 Su-25's with mixed armament you would now just have to take your chances 3 Su-25 instead of four approaching enemy fire. So, in my personal opinion, the Yak-130 could still have a place in front-line missions and be a cheap alternative, although not a replacement for CAS aircraft like the Su-25.
Or else Russia would have to consider the Yak-152. Start transferring the aircraft produced to DOSAAF hangars to effectively have a viable alternative in a war against UAVs launched on Russian territory.