I don't know what the Russians think. Not only the air force, I also wonder why the Russians did not directly attack Kharkov.
Kharkov is close to the border, so Russia can easily take advantage of artillery. Moreover, Kharkov is an industrial center and a population center. Kharkov is a Russian speaking area, and the locals are pro Russian. During WW2, Germany and the Soviet Union broke out in Kharkov to decide the ownership of Ukraine. If Russia chose Kharkov as its main attack direction instead of eastern Ukraine when the Ukrainian war broke out, the situation should be very different now.
Attack Kharkov to force the Ukrainian army to rescue, and use the air force to attack in the process of Ukrainian army transfer.
Is that one of you "expertise" again??
First of all, THEY HAD ATTACKED Kharkiv, and was beaten back, it was attacked on day 1 and the Ukrainian pushed them all the way back to 5 miles outside Russian Border back in May.
The problem is what Ukrainian had in the strategic crossing they hold the area that can sever the key GLOC toward the Eastern Donbas region. Which mean if the Russian wanted to keep on attacking, they will need to spread their force to protect their own supply line, meanwhile have to concentrate their force on attacking Donbas. If they push toward Kharkiv again, setting aside can that be done in a moment, that mean they will either have to stop the Donbas advance completely for months (that's how long the last attack last) which will give Ukrainian time to consolidate their line and pull in Reinforcement or they will have to thin out their protection along their Northern GLOC, which will open to counter attack, the risk is too much because you are risking the collapse of the entire Northern GLOC.
As for Airforce, it is not what you have, but how are you going to use it, first of all, a lot of their Airforce is static element, which are needed to guard the airspace toward Japan, South Korea, Poland, Finland, even if you say China will not attack Russia and Russia are allowed to pull every aircraft in operation there, you are talking about 100-200 combat aircraft can be used at anytime. Of the 1500 aircraft on paper, 300+ of those are Transport, another 200+ is trainer and other aircraft, only leave about 800-900 Fighter/Attacker aircraft, half of those are old Su-24/Su-25. Secondly, Russia do not have stealth aircraft not any combat support aircraft beside AWACS, and they are facing a peer or near peer air defence power. Which mean you are seriously risking being shot down (and 40 Russian fighter did got shot down) when you penetrate thru the Ukrainian Airspace.