I'm not removing it as irrelevant from all things. I'm saying its irrelevant as part of a discussion for what other traits define many and/or are exclusively manly.

I'm not really sure what you're asking with ,"is your assertion that a woman or enby would use the word “manly” to describe and identity of being a responsible adult?"

For sure I'm not looking for a single authoritative definition. I am, in fact rejecting just about any definition or even the need for one. I am, at the end of my logic train, begging the question, "why does it even matter?" I certainly don't care if society deems me "a man" or "manly". I don't judge other people by such a rubric. I think society would be better off if we work to actively reject such notions since they lead to gatekeeping which is rarely helpful. All that matters is that I'm happy with who I am, within the bounds of whatever it means to also being good to other people.

Obviously that opinion means it will be very hard for someone to come up with examples of traits* that are actually really honestly unique to man/male-ness which a woman can't/won't/shouldn't also possess as part of being a good responsible person? I have yet to hear any. They ALL a equally true for a good person regardless of gender / gender identity.

*In this context I will concede the obvious biological function you've pointed out, while at the same time ignoring it as irrelevant because it can stand on it's own AND have no impact on the other traits being discussed. Just because someone "handles themselves like an adult and happens to be male" doesn't in mean it logically follows that handling oneself as an adult = male. Just like the equally valid sentence, "handles themselves like an adult and happens to be female" doesn't make handling oneself as an adult = female. They just mean you're a responsible adult and not an irresponsible child.