What's the point of gender reassignment surgery which doesn't change a person's chromosomes?

The single thing that does determine sex is the SRY gene. Its discovery in 1990 changed everything science thought it knew about sex in placental mammals.

In other words, these different levels don’t always sync-up. It is possible for your brain, your body, and your genetics to have different biological sexes.

This can include the SRY gene being defective, being blocked by other mutations, being on the X chromosome instead of the Y, or missing altogether.

Why do men always bring up “the draft” (the last military draft was in 1972) when abortion rights are being discussed? - are they advocating that women ought to owe our bodies to the government? Should anyone owe their body to the state?

It doesn’t have to change chromosomes, because chromosomes do not determine sex.

All of these variations have an effect on the person’s neuropsychology and thus their experience of their sex & gender.

It’s usually found at the tip of the Y chromosome (which is why we thought sex was in chromosomes), but there are a number of variations that will change a person’s anatomical sex, neurological sex, chromosomal sex, and genetic sex.

The Simple Rule That Seems To Govern How Life Is Organized On Earth - IFLScience

So what happens inside “gender-affirming care” depends upon the patient’s lived experience. However, it’s been demonstrated conclusively by a century of psychiatry trying to change transgender patients’ gender identity to match their physical anatomy does not work and in most cases only worsens their mental health, especially in minors.

Corollary: sex and gender in humans is actually floridly-complex and occasionally very messy.