Wait, does that mean there are no flights to Ukraine at all? Or is it mostly over the war zone in the east?

To answer the question of what has taken the place of air travel, domestic within as well as international mass transport to and from Ukraine has been predominantly train based during the most recent invasion:

https://apnews.com/article/russia-ukraine-war-riding-the-rai...

https://apnews.com/article/poland-railway-disruptions-arrest...

No flights at all. See it yourself https://www.flightradar24.com/