I've never heard that before. Do you have a source for that information?
Athenian democracy was more like "democracy for wealthy athenian landowners." It's not much like modern democracy, so there was a lot to criticize about it. Even modern democracy can be described as "rule of the ignorant" in some places, so it's not like it's impossible to validly criticize.
I don't know what kinds of arguments Jordan Peterson makes because I've never listened to him, but from what I've heard it sounds like he merely tries to rationalize male stereotypes by giving them an appearance of validity. That's definitely not what Socrates was doing; in fact the Athenian elites he criticized were closer to the Jordan Peterson type.
And nothing Socrates or Plato said remotely resembled Nazi propaganda, so unless you cite some textual examples I'm not going to take that seriously.
Also, Plato criticized the 30 tyrants. So I don't see what connection you're trying to draw there.
As far as "non-Platonic contemporary accounts" go, what primary sources are they citing? Or is it just pure navel-gazing? Criticizing old white dudes is the easiest way to get ahead in modern academia, it's the only way to slide through the peer-review process without a defensible critique. Valid criticisms can be made, but they require textual evidence (unless they're criticizing a white dude; then anything goes, apparently).
Sophists made use of wordplay and tautology to seem wise, while mostly reaffirming common assumptions that people already held. Plato and Socrates were rationalists, which is completely different. They used discursive reasoning rather than mere semantics. And if someone doesn't understand the difference, then it's not worth my time to try to explain. Too many people reject rationalism while falling for semantics; how does one reason with someone who's irrational?