Ginga Kikoutai Majestic Prince

Interested in the genre? Despite what people might say, mecha is a rich character focused genre with a variety of incredibly unique stories to tell. Here's a collection of shows with short, straight-to-the-point descriptions about each. Note that some of these were translated by fans, and aren't available officially/legally. A good amount of these are available on various streaming services, tho as for all well you might have to sail the high seas a bit. Disregard my personal scores, as its subjective at end of the day and you might like it. Also please don't dismiss some of these just because they're really old, they pretty much all hold up well even today. Check each out, and see what strikes your fancy. Any shows I personally haven't watch I got info on from fellow mecha friends of mine:

These are the anime that appear in Super Robot Wars 30 for PS4, Switch, and Steam on PC.

These are the anime that appear in Super Robot Wars X-Ω, a mobile phone game that is now defunct.
It's being split into multiple parts because there are so many.
I promise you that nothing on this stack is a joke.

The Classical Generic Mecha When Done Right Lead To Such Amazing Shows.

To qualify for this stack, the following must be true

1) The show includes some form of mecha, interpreted loosely.
2) The show must include one or more important female characters
3) At least one of the female characters, other than a villain, must interact directly with the mecha in an important role (typically pilot, but other roles can be sufficient)

This does not require that only females pilot or even that the main character/pilot must be female, only that we get a good active role from a female character, not just a damsel or sideline role.