Plus if you are not in an a t m o s p h e r i c mood, you can watch Moscow - Cassiopeia (kids space film) and Kuryer (coming of age comedic drama in EOL CCCP) instead.
And then The War of the Worlds: Next Century with Iron Idem for dark comedy that's even less a fan of Soviet stuff
But I saw Katya as a distant, hidden ideal for Ivan. In terms of her reflection on him being hidden from his consciousness.
She's far more idealistic in terms of silent goodness / valuing mindset. This is like the Stanislav Kurilov mindset. Calm, but knowing deeply that things like repression and conscription for short-sighted power goals are not ultimately acceptable.
Refined in character, nearly angelic, but how? And what does it mean? This is Ivan's unconscious puzzle.
To her, he seems to ground her. She understands him almost as a pet, so this perhaps explains a bit. But in this situation she can't yet express to him fully what the above implies for him. Her deeper consciousness is not available to him.
IMO this is where we got a lot of the emergent criminality in the 90s chaos (beyond what existed already), this disconnect. Those who can make values conscious but who will not force the message, formed the moralistic vitality of change. And those who will take action but who do not naturally tend to values form the vitality of force seeking direction. This contributes to broad chaos toward a structural vacuum. Something must be done in the idea space in order to propagate the values further. A very difficult problem for most of humanity at this point in time.
Just some thoughts though. Hope I understood some of what you were getting at. Please share your own thoughts if you would like.
Something that did strike me is that, as a teenager on the other side of the iron curtain, I had been chasing girls at the local residential private school, who introduced me to anime — so the scene where Katya's friends are watching live-action japanese media seemed like a nice parallel (at least post-Glasnost) in our lives.