but if someone takes away societal gender norms, and takes away body dysmorphia, what is “left” to define gender as?

I mean, this is becoming so hypothetical. You assume that taking away gender norms is possible or even desired. I don't know the latest research, but as far as I understand it's not certain that there's 0 biological component to gender expression. Like another poster mentioned, people are tied to their gender. They like how they express it.

And furthermore, "removing body [dysphoria]" is hand waving away a LOT. That's the primary reason people transition. But it's tied into how society views gender, and that view is at least informed by biology. So extracting that isn't a useful exercise imo. It's possible that in a different society that doesn't differentiate between gender, then trans people wouldn't feel a need to transition. But yeah I don't know how that would be a helpful thing to think about.

this isn’t a challenge to your existence or anything else meant to make you feel uncomfortable

Full disclosure, I have decided not to transition. And I'm hesitant to call myself trans only because I think that label comes with a lot of implications for how the world treats you, and I would feel that I'm co-opting the term. So I'm basically coming from the place of someone with dysphoria.

Because to be honest, I actually don't relate much with the trans people like the post in the OP who liked stereotypically girly things as a kid. But now I wonder if that was because I felt I couldn't, or I would be judged, or just because I happen to not like those things. I don't really know where I'm going with this. But I guess my point is, you're asking for a logical explanation and concrete rules. And that's just not possible to give because many trans people don't even know themselves what "being a woman" or "being a man" actually means. Just that something is wrong. And there's not a simple fix. It's not just a matter of clothes, because whenever I see myself in women's clothes it actually makes my dsyphoria worse. Because all you see in the mirror is a man in a dress, not a woman ( a common feeling https://www.reddit.com/r/asktransgender/comments/vz3qlf/overcoming_man_on_a_dress_feeling/ ). And it's not about your interests, because as you correctly point out, girls are totally free to like "boy" things and vice versa, and that doesn't and shouldn't necessarily imply they're trans.