it’s not like anyone, cis or trans, is ontologically a man or woman.

I completely, 100% have to disagree. I am very definitely ontologically a woman. It is just that Woman is neither a category of biology (that would be "female") nor a social role (that would be "feminine"), it is rather an internal, psychological category relating to our sense of self. It is the frame of reference through which we perceive the entire rest of our gender experience, the relationship to our bodies, the gendered relationships to other human beings, our gender performance, the relation between our behavior and gendered expectations ("do i like this because i'm a man or do i like it in spite of being a girl?"), the framing of our sexual orientation ("am i a straight man or a lesbian woman?") and so on.

Reducing gender to a two-fold model that just knows biological sex and gender as a social construct does not explain my experience at all, nor does it explain the experience of a majority of other trans people. It is beyond discussion to me that it is empirically non-viable. Focussing too much on a fleeting, socially constructed, idealist concept like gender performance is indeed a red herring when exploring one's gender, just as it is a mistake to get hung up on someting that can be changed just by hitting the right hormonal switches at the right moments like biology. To make sense of our lifes, especially that it is to us undeniably self-evident that we have never been our assigned gender at birth even when we supressed it and performed in a different gender role, in a body mismatched with our self, only makes sense when you treat woman or man or enbie as a seperate, internal category, everybody's "true self" so to speak. Otherwise, if i had a male body for most of my life and performed as a boy for most of my life, which i had and which i did, how could i always have been trans? I would have started being trans when my egg cracked, but not before, because under a two-dimensional biological + social model, 100% of the dimensions of my gender experience would have been manly. But they weren't. Neither my body nor my role as a boy ever fit me. Nothing in my life ever made sense, it was all a disparate jumble of struggling to fit a mold not made for me - and once i realised "oh, i'm just trans", all of that stopped. It just turned to dust. It could not offer the slightest resistance. Everything made sense by simply fitting in that missing puzzle piece that was my gender identity. This is a quite common experience for trans people who do not fall in the "i've always known, i refused to wear pants when i was just three years old and then i told mom it's a mistake by god that i have a weenie" category - lots of trans people do see their true self as early as that, lots of others don't and instead only come out later in life, but evidence clearly shows we're all equally valid.

Not feeling that you even have a gender identity is ofc still possible - it is a logical conclusion for agender people where gender identity may just be a blank, it may also be a privilege of cis people who never had to think about this issue too hard because their gender identity, social gender role and biological sex are all more or less completely aligned from the start, or it may be a fairly typical train of thought for eggs who through their denial and repression lack a connection with their gender identity (the latter was me for a large part of my life).

But if you want to explain everybody's gender experience - and a viable gender theory should do exactly that - you need more than the two dimensions of biology and social role. What i've outlined here is based on Leslie Feinberg's model, i've also seen five-fold models. But regardless of what you use, two-fold is always too simplistic, it is only an intermediary step up from bio-reductionist explanations like "gender is just your chromosomes".