I like the idea of giving WW a classification of enemies that are more distinctly hers than Batman's or Superman's. Whether the Greek pantheon works for that or not (and they've made worse ideas work in comics), the rationale behind the idea is a good one.
I also really like the ideas for her equipment. This lets her still be "peak Amazon" as it was put but also more than that but without a contrived reason. She's a princess. She should get given the best toys.
My own way to distinguish her from Superman and Batman, back in the thread somewhere, was in terms of morality and personality. She's the only one of the three who is a soldier. The only one who is openly a warrior. Superman is great and honourable but he's a civilian in many ways, an ordinary person doing his civic duty to help because he can. Batman is the opposite - no special powers but he is far from ordinary. But he is also not a soldier, not even a special ops sort. He's a rogue agent, a half-criminal himself. If you had to give him an equivalent job role he'd be more like a CIA agent or a deep cover detective, living on the line. He can fight, but he's not a soldier.
Diana is the warrior-soldier. She uses a sword, a killing weapon. She isn't a martial artist like Batman, she's trained to fight alongside her sisters in battle formation. You put this role alongside Batman and Superman and you have all sorts of nice demarcations.
Superman: face, leadership, presidential, humble, extraordinary threats to the planet, inspirational and approachable.
Batman: intelligence, deception, frightening, extreme, equipped to deal with murderers and psychopaths, street and organized crime, undercover.
Wonder Woman: Military liaison, politically adept, tactician, dispatcher of threats with lethal force - morally uncontroversial because she's a soldier and fighting neither petty crooks nor an unappointed civillian, but rather fighting enemies that would probably be classed as an invading force. She can draw on Batman for Intelligence. She can defer to Superman as the charismatic public leader who whilst not naive, strives to keep his hands clean.
I guess this is in some ways my own variant on
@BubbaRobot887 's Greek gods idea - both seeking some defining her as different through having different enemies. Though mine is more of a general theme than a specific. Batman isn't going to fight alongside the army (or shouldn't), Superman also is someone who is there to rescue and protect, not to participate. Diana is the earthly one who you could see standing around a table with generals discussing how to defeat the invading Byalian forces that Darkseid or Ares or Intergang have subverted as proxies. Things like that.
EDIT:
What she needs is apprentices. Have her train Amazons in interacting with the rest of the world. Have them meet Steve, his team of soldiers, women in power, other supers etc etc. Showing WW through the eyes of someone new can be rejuvenating. She needs better cast. Batman's continued popularity is partly due to his extended family and his chemistry with them. Have that happen with WW.
Build out her supporting cast of soldiers and army types. She already has a natural path into that with both Steve Trevor and her role as a political figure. A four star general may not be able to punch a whole in concrete but he's a powerful figure who can talk to her on her level.
