Kyiv has never been under siege. The Russians failed at encircling Kyiv, and at this point do not have the manpower or capability to do it, so they’ve just been chucking bombs into the city, targeting foodstores, warehouses, government buildings, etc.
They were constantly attacking down the west side of Kiev, at one point last week cutting the direct highway Lviv-Kiev. But that seems to have stopped and the Ukes have the highway back.