I don't think there has ever been a real proof, and I vaguely recall some reasonable argument it was actually 33%. But I may be misremembering or wrong.

In the literature they generally accept 51% for PoW but put a big * next to it, since it has been proven that there are ways to circumvent safety with much less already (25% for selfish mining) and there is a certain mathematical probability to get even worse done with 25%.
PoW is more "probably 51%". In PoS since the node is chosen deterministically I don't see why 51% could be a big problem. But I also didn't read any "real mathematical proof" for it yet either.
Classical BFT is only 33% because of asynchronous network conditions, under synchronicity it can do 2f+1 (51%) as well.

If you have further analysis I'm interested to see it. In my view 30 being well over 20 is probably somewhat okay because it allows coverage to all acceptable primaries (which should tend to overlap a lot among reasonable stakeholders) as well as some backups. But without a stronger argument than that, confidence can't be too high. If we could gain significantly by increasing 30 to say 50, I don't think the downsides would be that serious and we should consider it.

I'll check if I can get a reasonable analysis out of it. Unfortunately most of it is more based on game-theory and crowd behavior and is not very deterministic. Like "People are more likely to vote on people which are on the top of the list already anyway".