Correct; FTM transition.

If that’s the case, first of all isn’t it relevant to a doctor that you take hormones? One of the first questions most doctors ask is if you’re on any prescription, and to a doctor wouldn’t your genetics+hormones give a more correct picture than either male or female would?

I absolutely agree with you here. A holistic understanding is infinitely more useful than any one-liner or discrete classification; this is true of everything, not just sex. However, the reason we have sex as a binary classification for patient data is because for 99% of patients this is more succinct (and therefore time-saving) for doctors, than going through a medical history to determine hormone profile and organ inventory, etc. In an ideal world, these factors should be considered carefully for all patients, not just those they perceive to be ’outliers’ in some way.

It might be ignorance on my part but I can’t see a situation in which being medically treated as a female would be life threatening, but I can see several where being treated as a male would.

Reference ranges for blood testing is the most pertinent example. Interpreting the results w.r.t a female baseline would be misguided and cause them to miss certain anomalies, causing delays if not outright blocking diagnosis and treatment. That can be life-threatening depending on the specific condition. The opposite can happen too, i.e. a false positive, when the result is normal for men.

Hospital wards are split by gender not sex, so you should still be put into a male one.

This is unfortunately no longer true in the UK as of yesterday.