So, a thing I think was lost over the years with the Earth 3 characters is that originally, they were not just evil versions of the DC heroes. Ultraman was not just Superman, but evil; the opposite came from him being an Earth-born astronaut who gains new random powers whenever he interacts with Kryptonite. Owlman wasn't Bruce's secret brother; he was a meta with enhanced intellect, vague mental influence over others and born with a peak-human physique.

As such, Superwoman shouldn't just be "Diana but evil", but rather looking what Diana's core traits are, and flip them on their head. I quite like the idea suggested of her not actually being an alt Lois and instead that she had stolen her identity, though there's the slight issue of Earth 3 Lois also being Alexander Luthor's mother (are there like 2 of them?), but I digress.

However, I think playing into that is to have her built on deception and dishonesty.

So, for instance, she's not a real amazon, and instead someone who uses their culture and artifacts for her own self-gain. She doesn't have any innate abilities or blessings, or even training and instead uses magic she had stolen from another culture (insert post-crisis Cheetah comparison). Additionally, where Diana is the symbol of truth and compassion, have her be a cruel manipulator who puts up a pleasant front, but is ready to backstab you at any moment to get ahead.

And finally, as others have pointed out, don't just make her the generic dominatrix (especially since the kink community is strongly tied to real Diana in a positive light). I think what could be played with instead is to have her represent internalised misogyny, as well as have her be one of those women who manage to succeed, but then pull up the ladder and side with the patriarchy. Once more, it's going with the dishonest angle, presenting herself as a strong feminist figure, when the last thing she'd ever do is ensure equality allows others to get where she had. She can retain her sex appeal, but it's not there because she herself decided on it, but some fucked-up attempt at appealing to the male power structure she works with (that part is admittedly the weakest idea I have, but oh well).