I'm not sure what you believe this question is getting at.
We divide up chickens (and all livestock) according to genitalia. So if you applied the same metric to people, that would mean GRS does indeed change the biological sex.
Well, now we are getting to the problem of using the term biological sex instead of sex that's assigned at birth
Eg. A lot of these states are pretending assigned at birth sex is the same as biological sex. The sex on your birth certificate is not necessarily your biological sex. It's just what the doctor gave you by looking at your genetalia at birth with no further investigations. This seems like the worst way to seperate a sporting league
Conservatives use these interchangeablely and thus inappropriately sometimes. They are two different but not mutually exclusive things. What is written on your birth certificate is NOT your biological sex
Anyway, biological sex is based on gametes. Thus, bunch of people don't qualify as either biological sex. You can be born without eggs or ability to make sper.. Then you have transpeople who, as an end goal, (currently) don't produce gametes either
Note: gametes have nothing to do with sports performance. Hence me thinking it's really stupid basing sports competition on whether you can produce gametes or not
So, I don't agree with your biological sex assessment here. You're talking about morphological sex. You will never here about this from transphobes. It's an automatic loss for them. That's why they focus on biological sex exclusively. They're just trying to control the narrative.
And things like sports performance isn't related to your genetalia either. Even basing your league criteria on this is stupid. Nor is your assigned sex. This is just a ploy by some to confuse the issue