Where is the admonishment that men should do the same?

Ephesus is not a patriarchal society. You are still assuming a culture and context that is equivalent to your own modern experience. Women are a privileged class in 200 CE Ephesus, and had been for hundreds of years. Like all privileged classes in all of human history, they are the group that are most likely to try to seize authority for themselves. Parading ostentatious wealth in the form of fancy hair, jewelry, and expensive clothes was not a trait of Ephesian men, but Ephesian women.

Also "a woman" and "a man" does not mean "every woman" or "every man", or even "any woman" or "any man." It is a targeted reference to the specific issue that Timothy was dealing with in Ephesus... Artemis adherents trying to take control of the fledgling christian cult, even though they don't know the first thing about them or their doctrine. The Koine offers a lot of clear meaning and intent that is very difficult to convey in either English or terms that are understandable to a modern person with no historical frame of reference.

What Paul is saying is "If women want to teach, they first need to learn. If they want to learn, they need to stop flaunting their wealth, stop behaving like entitled jerks, and start treating our teachers — who are men — with respect, instead of trying to usurp their positions. We aren't doing this for clout, but to improve everyone's lives. Those who haven't learned the rules are going to make terrible mistakes."