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

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

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.

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.

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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.

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.

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

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

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.