I get where you are coming from on this, and I think some of the 'analyses' in media headlines don't help. I've been frustrated by the number of headlines and commentators saying things like 'women are defined by their biological sex', because that phraseology is depressingly reductive.
But (thankfully) that isn't what the SC judgment said. It said that, for the purposes of the Equality Act, the WORD 'woman' is defined in terms of biological sex as an adult human female. For the rule of law to work, it needs to be based on clear definitions of the words it is written with. If we don't have that, we have nothing. [And in fact the lack of common understanding of what words mean is a major obstacle in effective dialogue on matters of sex/gender. It's almost as if some people don't want there to be clarity...]
So for the purposes of assessing whether or not something constitutes sex discrimination, the determining factor is biological sex. And, for the purposes of defining whether something falls within the single sex exemptions in the Act (i.e. places where it is lawful to treat one sex differently from the other), the determining factor is biological sex.
This is good. This clarification confirms that the protections against sex discrimination, which were put in place as recently as 1975 (1976 in Northern Ireland), remain intact and have not been eroded. For those of us who belong to the sex class that has traditionally been seen as second class, this is really important because those protections remain valuable.*
Thankfully, we are all more than the sum of our parts. Those of us who are gender non-conforming women have been fighting against reductionist gender stereotypes all our lives. We don't necessarily have a 'gender identity' (although I accept some people believe they have one, just as some people have religious beliefs, which are real to them even if they are unprovable to the rest of us), but neither does our sex determine all aspects of our personality or imposes limitations on (eg) our career ambitions or our hobbies or interests.
*The protections on grounds of sex are, of course, not the only ones in the Equality Act. For trans people, the protected characteristic of gender reassignment is vital in protecting them from discrimination. Those are undiminished by the SC ruling. If more is needed in order for trans people to live their lives safely, then that is a discussion to be had - in a grown up way, not through hyperbole about denying people's existence, demanding their erasure, literal genocide etc... But their protection cannot happen at the expense of the sex-based protection of women.
[Sorry that was long!]