Another thing to remember is turkey has been stepping on Russia’s toes for quite a while now. The Turkish invasion of Syria (to slaughter the Kurds) and the Turkish backed assault to retake that border region in Armenia are two recent events that come to mind.
A nato member is trying to assert its dominance over areas that have historically been under the Russian sphere of influence. Russia can rightfully see that as provocation on the part of nato. There were no condemnations, strongly worded warnings, or sanctions issued by any of nato over these acts of aggression, which clearly means the rest of them approve of turkey’s actions.
So maybe Putin is looking to seize a little more territory from the Ukraine in retaliation for this. Call it a demilitarized safe zone or some shit like that, to protect their people from unwarranted attacks by the evil Ukrainians. But in reality he and everyone involved in nato know that it was his way of pushing back against the incursions into his sphere of influence without engaging in a large scale conflict or directly attack a nato member. Just to let us know he’s still there, and he’s not to be fucked with.