And it feels just wholey wrong to say “gender dysphoria is internalized misogyny” but I can’t put my finger on why. Or how they’re linked or if they’re not.

Because the individual component parts of gender dysphoria, the little needles from this or that feature or action or idea, aren't in and of themselves unique to the trans experience. I've argued this before, but I firmly believe that a big part of what gender is neurologically is more of a filter on socialization and development of self-image than a hard setting, like it's grabbing bits of culture you're exposed to and saying "this image/role is for me" or "this image/role is not for me" based on context and layering that down to form one's own perception of oneself and one's gender.

That means that functionally cis people also experience elements of gender dysphoria when dealing with things they've internalized as being "wrong" for their own gender, it's just they experience fewer of these and with less intensity than trans people do.

It also means that gender in terms of culture is both constructed but also real: it's a malleable and learned collection of concepts and images, but one which we necessarily internalize and form into less malleable structures in our own minds. We exist within the cultural context that we were raised in and have limited ability to drastically change it, especially as individuals, so as I see it our priority should be mitigating the most harmful elements of it and liberating ourselves from it insofar as we can, but accepting that it has left its mark on us in an indelible way and understanding that we are still existing in a society hegemonically dominated by that same toxic cisheteronormative patriarchal culture.

Like we can say "things should be better! we must abolish all these old ideals and aesthetics as gendered things and so liberate everyone to develop on their own and take their own path!" but that's not the reality we have to work with, we cannot simply declare gender to be fake and dismiss all the things we've internalized in one fell swoop because even if we materially had the power to make that the new cultural hegemony overnight it's not how our brains work regardless. All we can really do is focus on LGBT and women's rights as policy and as individuals work on gradually shifting the internalized things that bother us the most (if we even want to - I have absolutely no desire to disentangle having long hair from my gender identity even if it's pathological how traumatic I find having it cut even slightly, for example).