What does it really mean to say "trans-women are women"? A TERF-y but genuine question.

Warning: Standard cis straight white male here.

Warning: I'm somewhat well versed in the standard trans-rights feminist position, and I lean pretty strongly pro trans rights, but I think I might still have some TERF streaks in me as well. I am just trying to understand the standard pro trans rights position more clearly, because it confuses me.

I need to lay out some framework before I can ask the question. Sorry.

I hope I can take for granted that I can talk about biological sex as multi-dimensional distribution of humans, of which about 99%+ fit nicely into two distinct camps, biologically male and biologically female. Aka bi-modal. The dimensions include chromosomes, genitals, secondary sex characteristics (i.e. breasts). Not everyone in either group has all of the defining characteristics, but 99%+ of the population fits nicely into one of the two buckets. There are some people who don't fit into the one of the two buckets, e.g. intersex people.

I understand what "gender" is in terms of gender roles. There is the man gender role and the woman gender role. For example, men wear pants and women wear skirts. For example, men are workers and women are stay-at-home moms. These are examples of gender roles. Gender roles are social constructs, with very little to no basis in genetics. For example, there is nothing in genetics that says that males like blue and females like pink. Furthermore, gender roles can and do change over time in some small ways, i.e. IIRC toys for boys were typically pink like 150 years ago.

Some people believe that there are significant behavioral differences between the biological sexes because of genetic differences causing differences in brain development. Let's call this "gender essentialism". Gender essentialism can be true even if a significant portion of behavioral differences between biological males and biological females are due to upbringing. Gender essentialism is the hypothesis that at least some non-negligible amount of behavioral differences between biological males and females. I happen to think that gender essentialism is basically false.

Now this is where it might start getting TERF-y.

I understand one of the major goals of feminism to be the destruction of socially enforced gender roles. Socially enforced gender roles are a bad thing.

I know that trans-women are not literally claiming that they are biologically female. I know that they're not claiming to have chromosomes, genitals, or secondary sex characteristics that they do not have. In other words, I know that they're not deluded and not insane.

However, I don't really know what a trans-woman means when they say "I am a woman". I have several guesses, working theories, which I'll share in a moment. I also suspect that I will get a difference answer for every trans-woman. Some answers might be complimentary.

Maybe a trans-woman means "I want to be treated like any other woman. I want to be referred to with feminine pronouns. I want to use the women's restrooms. Etc.". I understand that. I'm typically cool with that, with maybe very very minor exceptions which do make me run afoul of trans-rights activists (i.e. women's rape shelters, maybe sports, don't really care about restrooms), and that's why I think I'm a little TERF-y.

Maybe a trans-woman means "I instinctively feel like I am a woman, in a manner very similar to how you are instinctively are attracted to women as a normal cis straight man". This is harder for me to relate to. This is the part I don't get. I don't "feel like a man". I don't know what that means. Maybe it's my privilege. Dunno.

I'm not saying that a trans-woman is lying. I'm not even saying that they're mistaken.

Here are my questions.

What does it mean to say that "I feel like a woman" without reference to gender roles? Conversely, I totally understand what it might mean for someone to feel more comfortable being treated by others according to one of the two typical gender roles. However, without referencing gender roles, which I believe to be almost entirely arbitrary social constructs, what does it even mean to say "I feel like I am a woman"? I just don't understand what it means.

Similarly, the standard TERF argument still makes a lot of sense to me, namely: If the goal of feminism and social justice is the end of oppression of woman, and I'm totally on board with that goal, and the means by which women are oppressed in society is (current) gender roles, and I'm on board with that premise, then shouldn't our goal to be to denounce gender roles? But that's not the real question. The real question is: How can I understand what it means to be a trans-woman or a trans-man without appealing to (arbitrary, socially constructed) gender roles? And the best formulation I think is: Saying "I am a trans-woman" only really makes sense to me under the assumption of gender essentialism, the idea that there are inherent behavioral - and mental - differences between biological males and biological females. A trans-woman who says "I am a woman" makes sense to me if I assume that there are real, inherent, immutable, (genetic,) mental and behavioral differences between the typical man and woman. However, as a feminist, I thought that was precisely the move that I wasn't supposed to make.

Also, it's still confusing to me, because I've never felt like a man, and I don't even know what that might mean. I don't know what it means to say "I feel like I am a woman" or "I feel like I am a man". By contrast, I know what it means to be straight or bi or gay. I know what it means to be attracted to women and not men.

Technically, I understand what it means to say "I feel like a man" in terms of "I like how I am treated by others when others view me as a man and treat me according to established social gender norms", but I don't think this is sustainable and workable philosophically because of the reasons that I mentioned above. Specifically, gender norms are social constructs, and to say "I like being treated according to one gender norm" doesn't mean that they have some sort of feeling that they're the other gender/sex, but instead it's an attack on societal gender norms and gender roles.

Or, do trans-rights activists think that the eventual goal is something other than the destruction of gender roles and gender norms?

Similarly, the standard TERF argument still makes a lot of sense to me, namely: If the goal of feminism and social justice is the end of oppression of woman, and I'm totally on board with that goal, and the means by which women are oppressed in society is (current) gender roles, and I'm on board with that premise, then shouldn't our goal to be to denounce gender roles? But that's not the real question. The real question is: How can I understand what it means to be a trans-woman or a trans-man without appealing to (arbitrary, socially constructed) gender roles? And the best formulation I think is: Saying "I am a trans-woman" only really makes sense to me under the assumption of gender essentialism, the idea that there are inherent behavioral - and mental - differences between typical biological males and biological females. A trans-woman who says "I am a woman" makes sense to me if I assume that there are real, inherent, immutable, (genetic,) mental and behavioral differences between the typical man and woman. However, as a feminist, I thought that was precisely the move that I wasn't supposed to make.

EDIT: Did a mod just cut the last paragraph or two? Let me summarize: Thanks for any help and any resources (i.e. books, articles) that you can point me towards.