I don't think you're out of place in this.
I think your POV is important for a few reasons, too: what you're describing is something trans women often struggle with, but also something that many cisgender women do once they are peri/menopausal. There's a LOT out there that suggests periods = womanhood (a thing there is no end to my personal and professional complicated feelings about), so I'd say quite a lot of people struggle at one time or another with feeling like periods basically outright give or make or prove feminine sex or gender.
As I'm entering menopause, one thing I keep finding is that I certainly seem to feel differently about it than some of my peers in this regard: I don't and am not (not so far anyway) experiencing feeling like it's having any impact on my gender, but then I am and have always felt pretty genderqueer, and even in the ways or at the times I feel like/identify as a woman, I'd say that's more political than physical for me, if that makes sense. When it has been physical for me, my sense of physicality as a woman has generally not been particularly feminine, and also has not generally been connected (nor have my periods) with the ability to make babies, save as it impacts my health and my rights and lack of either.
(My periods also have been very painful and disruptive for almost four decades of my life, so them finally winding down and starting to give me a break is a net positive for me no matter what.)
It'll be interesting, I think, to see how I feel when I'm all the way at the end of it. Maybe it'll be the same, and all around have been something that just wasn't really about my gender and didn't play a part in my ideas about gender, but you never know: I may wind up finding out it had more of an impact than I thought.
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead