Same here as a guy. I don't usually self-insert, so I enjoy the story as it is.
I think the entire foundation of the story, the characterization of the cast, and the dynamics built around them would fall apart if the MC weren't a woman. The story, the experiences the MC goes through, how her personality is shaped, and the relationships she develops with other characters are all intentionally centered on her being a woman. Her gender isn't just a detail...it is a core part of the narrative.
The personalities of the other characters, their actions, the way they treat the MC, and the gender dynamics between them are all deliberately crafted around a female protagonist, reflecting heteronormative and heterosocial dynamics, expectations, and some rigid societal norms and stereotypes of that time and still today. It's clearly written from a woman's perspective/gaze. (Nothing wrong with that, I love women's works in fiction, but it won't always reflect different experiences, and some creators prefer to stick to what they like and have experienced. Others like to explore even if it's not personal to them. This game is very personal, as the creator stated.)
Those relationships weren't simply written for "a protagonist".. they were written specifically for a woman protagonist and what women experience. Replacing her with a non-woman protagonist would fundamentally alter those dynamics and, by extension, the story itself.
Especially because themes like misogyny, sexism, femicide, and GBV are integral to the game's narrative. They aren't just background elements. They actively shape the MC's personality, experiences, relationships, and development. I don't see the story working in the same way with a non-woman MC, because so much of its emotional and thematic weight comes from telling that story through a woman's perspective.
That's why I just enjoy it for what it is :3, without feeling the need to relate the MC to myself, and I agree with you