Okay, there is a lot to unpack here, and I kinda wanted to buy groceries now, so I'll make it quick.

but I was under the impression that which treatment a trans person needed was not reliably the one for a particular sex. That is to say, depending on what was troubling you, you might need either the male or the female version, or potentially even a secret third thing.

Yes, I was speaking generally about general tendencies in the simple case of binary trans people going through the typical “full” program. There are a lot of nuances, especially among nonbinary people, where this becomes more murky. But it's worth noting that the same holds for binary cis people, things are far from simple there either: As I wrote, sex is a bimodal distribution and if you assign people to the peak they are closer to, what I wrote will be a reasonable first approximation.

That said, I wouldn't consider that to be what makes you a woman.

That is a fair approach, I recently understood that I have kinda always rejected the notion of social gender roles on a pretty fundamental level, making it far more about outward biological characteristics more relevant.

So: “Yes, but…”

To me, "biological woman" is like "biological fish"; there is no set of biological characteristics that can determine with 100% accuracy whether a given animal fits into that group.

Yes. you always have a grey zone, but that notably doesn't invalidate the concept of a fish, it just means that we have to be aware that not everything fits perfectly.