Er, how would that differ? Its not like Barbie’s sex-assigned-at-birth is included on a certificate with the doll in the first place, or like the doll is so anatomically correct that one could determine what that likely was from the kind of genitalia and whether or not they had the telltale signs of surgical modification.
Various indicia are observed, sex (more accurately, “socially ascribed gender”, but the established terminology is “sex”) is assigned based on some subset of sex-related indicia.
> The modern construct of gender
The modern understanding of the distinction between sex, ascribed gender, and gender identity may be new, but the things themselves aren’t modern constructs. Biological sex (or at least the individual traits that make it up), socially ascribed gender, and gender identity have always existed.
This is an intentional and politically motivated conflation, that I notice you have attempted in several different threads, and it's why I replied here at all. Sex is a hard attribute that can be measured empirically at the chromosomal level, stop attempting to redefine it. https://en.wikipedia.org/wiki/Sex