There's only one definition throughout the Act.
Logically yes. They are accepting that biology defines sex when talking about SSS.
But for "all other purposes" men with a GRC are "legal women".
ie the law as written has created 2 definitions of women.
Which is exactly why there was a petition and a campaign to clarify the meaning of the word sex in the EA. And it did look as though Kemi Badenoch was moving towards bringing forward a bill (amendment?) to the EA to make it clear that sex means biological fact, not gender identity.
So on one level this is just about a badly worded bill that as time has moved on TRAs exploited.
Or those who believe in the influence of hidden networks, saw it as the result of pressure from TRAs to create a law that gives the minority (those with a GRC) the legal right to be regonised as the opposite sex.
Either way, with the passage of time, much as I, and I am sure others, would actually like it to be clearly stated in the EA that sex means biological reality, it wont actually stop those with a GRC demanding that their rights to be treated as the opposite sex are not undermined.
So in my mind,even if sex is defined as a biological fact, it probably means the SSE will still be needed because culturally so many people now think in terms of gender.
Added to which changing the definition of sex to only ever mean biological fact, would result in those with a GRC no longer being able to claim on passports or driving licences, let alone toilets, to be the opposite sex to the one they are born, GRCs become meaningless. If the change to the EA did go this far, there would be total melt down in the rainbow alliance, support be the still very large be kind brigade.
Many others have argued, (and i agree!) that the best most obvious changes to ensure there is no confusion is to scrap the GRA and GRCs.
This wouldn't stop anyone who wants to "live as the opposite sex" from doing that, but they can just get on with it without needing a certificate to say that they can. And even those who go down the path a medical "transitioning" could have pathways to doing that. But it would not result in a piece of paper stating they are the opposite sex to the one they were born.
However contermporary TRA campaigns are not necessarily about helping those who experience body dysmorphia, it is about a political victory for those who want to claim sex isn't real or set. ie harking back to the queer origins of current TRA objectives.