So sex in biology isn't usually identified via studying the chromosomes of an organism, since not even every species uses an XY Sex Determination system. It is generally determined via the primary and secondary sex characteristics exhibited by the organism. If the organism has female sex characteristics, they are "biologically female". Its get even murkier when discussing things like Klinefelter Syndrome, Swyer Syndrom, and de la Chapelle Syndrome.
There are people out there with XX Chromosomes that were born looking like men, have penises like men, sound like men, etc. And there are people out there with XY Chromosomes that were born looking like women. These people might not even be trans; it is just that genetics, biology, chromosomes and the like aren't so clear cut and easily put into two categories like "biologically male" and "biologically female".
The terms "biologically male" and "biologically female" tend to be phrases that exist within the realms of transphobes and the like to deny people's gender identities, and not anything used by scientists.
I can't speak for other states but in Texas early voting means you can vote at any polling place in your county. They reduce the amount of available polling places on actual election day, and you must vote at the polling place for your precinct only as well. So you're more likely to have less of a wait time than on election day, and thus it'll be easier to do.