@awnlee jawking
My understanding is that Russia quickly established aerial superiority but the good guys supplied Ukraine with anti-aircraft missiles and Russia was losing too many aircraft.
It's a bit more mixed than that from what I understood.
The Russians did manage to get the Ukrainian Air Force to abandon the skies for the most part, but not completely. That also didn't mean the Russians had establish aerial superiority in the sense that "they controlled the skies."
The Russians also failed to completely remove the (older) Soviet Era Air Defense systems that Ukraine still has. Evidently Russia cannot easily overcome even older versions of their own systems.
Much of Russia's much vaunted "precision weaponry" has also been shown to not be very precise by western standards. (anecdotally, I have second hand accounts of some (prior service) Americans helping to extract civilians from Russian controlled territory where they spent a night getting bombarded with limited artillery and even cruise missiles from the Russian Navy, with the fire being directed by a Russian Drone flying over head. The closest Russian attack landed 200 yards away from where they were. One of the attacks even left a crater 7 feet deep)
That lack of precision weapons leads to the next item.
Because they're lacking in precision weaponry for use by the Russian Air Forces so that they could attack from range(like NATO/the US would do), they've been using jets as "dumb bomb" delivery platforms.
The problem with using dumb bombs for close air support is it means you have to fly "low and slow" to minimize variables that could screw with the targeting... Which puts them inside the range of Surface to Air Missiles. And as such, the Russians have been getting a bunch of jets shot down over Ukraine.
But getting back to the matter that Russia can't seem to disable all of those Cold War Era S-300 batteries the Ukranians have that the allied forces handily destroyed in Desert Storm back in 1991?
Because they know several of those are "out in the wild" and under Ukranian Control, they have to operate "below the horizon" for the S-300 Radar Control systems of risk being shot down by those. Which limits how high they can fly before risking detection from a considerable range.
Too high, and a S-300 shoots you. Too low, and a SAM shoots you. But since you can't be certain where either a S-300 or SAM is likely to turn up, knowing exactly where those "grey zones" are at is problematic at best. As they can never be certain as to where the remaining S-300 systems are.
Ukraine has a comparable problem on their end, between Russian S-300, S-400, S-500 and other associated systems as well as their Airforce, any surviving aircraft of the Ukrainian's have to also be careful of where and when they go flying around the place.
Basically so far as the air war goes, it's a Mexican standoff where neither side can make effective use of large scale air warfare capabilities. Except Russia has been more willing to take risks as the nation with the larger equipment/manpower pool at the onset. NATO flooding Ukraine with assorted SAM platforms just further perpetuates the problem for the Russians.