Your understanding of sex does not encapsulate how transition changes a person’s sexual characteristics and organs, which are absolutely medically relevant information.

If I were reduced to my birth sex when e.g. admitted to a hospital, doctors would have a hard time figuring out how to treat me as I am very obviously different from that. The whole picture is important.

There is no such thing as 'biological sex' or, as you put it, sex as part of your basic biology, like some sort of immutable biological property each individual gets alongside other biological traits, such as eye or hair color. Like something you cannot discuss because it would be like discussing how many fingers you have on your hand. Sex is a classification made by humans based on some loosely grouped and kind of varying physical traits, which are even not always used consistently to tell sexes apart.

The first argument in defense of biological sex is that people with a penis and testicles are inherently and biologically men and people with a vulva and vagina are biologically women. But, you know, even when they are not common, there are people who have both or none in varying degrees. This usually turns to "women are people with XX chromosomes and men are people with XY chromosomes". But people with XXY chromosomes (Klinefelter syndrome) and just X chromosomes (Turner syndrome) also exist. You may say those people will be men or women based on what their physical development will make them look like. But you can already see how this starts taking sex assignment into some subjective area and not a basic biology property anymore. Then, you also have De La Chapelle syndrome and Swyer syndrome, which are people with XX chromosomes developing physical traits traditionally considered male and people with XY chromosomes developing physical traits traditionally considered female, respectively. We can continue going over the dozens of different conditions that make it impossible to tell that someone has one unquestionable basic biological sex. You could tell those cases are very rare (if you consider 1 % of the population as very rare), but they do exist. And, since you want to appeal to biology, in science you cannot simply ignore a scenario because it's not favourable for you and claim that your theory still holds because it works for the majority. Sex is a spectrum and sex binarism is a social construct: https://doi.org/10.1038/518288a

The same way that there is also no such thing as "biological race" and I thought that debate was over decades ago: https://bioanth.org/wp-content/uploads/2024/02/AAPA_Biological_Race_1996.pdf

Once you start questioning the idea of sex and race as basic biology that cannot be argued, you start seeing how those ideas are harder to sustain and insisting in doing so will place you in, let's say, uncomfortable positions.