But where was this propaganda coming from?

In general, people who don't know about something are often phobic to that something, so people were homophobic on their own, but police, Stalin personally (future general secretars were not claiming such directly, only through media) and KGB (previously NKVD) were promoting the idea about "homosexuality can spread" and "if you love men, they must be women" in masses (similar to some TRA ideas: https://saidit.net/s/LGBDropTheT/comments/796h/_/rfis). Idea about "if homosexual is not woman and denies transition, than this homosexual is just a pervert and paedo" was promoted later by KGB, when many paedo crimes were recorded as gay crimes - like Chikatilo crimes, so those criminals were doing their crimes uninvestigated. This part you already know, thought, as you watched "Citizen X" movie.

Nowadays in most post-USSR countries it is promoted because they want to be "the opposite of USA", so if USA saying "homosexuality can't be spread", then official TV channels are saying "USA want to promote homosexuality on your sons, we should block their influence/propaganda on us with censorship to save our sons and marriages!", implying that heterosexual men can become homosexual under TV influence. I don't remember it was mentioned directly that it can spread, unlike how it was in USSR. At the same time, progress is still moving on and people are not as homophobic and not listening to TV that much, even under propaganda.

Can you provide some links showing that this is really true?

I don't think I can, as it was just something I've been noticing in younger people discussions, memes about difference between 5'11" and 6'0", and general attitude. It can be a new thing among youth, but I've started noticing it 5-7 years ago, so maybe it is when it was started. I was not interested in this much, just something I was observing passively - maybe it is state specific, or demographics specific (or tied with racism, as on my memory most receivers of it were asian men around age of 16-25). I will try to focus my attention more on this, next time I'll encounter it.