Given that the context of the GRA was geared towards ‘old school’ transsexuals (i.e. before online gender woo), I would imagine this was born of the notion many male doctors would have had in gender medicine - that women are mere objects that can be replicated on the body of a man, and that it’s possible for a man to look ‘completely’ like a woman and to fool anyone, because those male doctors (who probably didn’t have the same evolutionary traits of sex-recognition that women had to develop out of necessity to survive) saw a man with a boob job and a bit of facial surgery and a dress as indistinguishable from an actual women. People pushing these sexist ideas and surgeries likely wouldn’t have been listening to what actual women thought anyway, not least as most of the old school cohort of transwomen were likely trying to attract a husband rather than a wife.
Also, those transsexuals who all trod the same established, onerous and detailed medical and surgical treatment path probably did pass far better than the average trans person, who typically eschews surgeries (and sometimes hormones) does today.
The notion of privacy in terms of gender reassignment only genuinely arises in people who actually pass, and I suspect the modern insistence on pronouns, not misgendering or deadnaming, and TWAW is designed to bridge the gap between passing and not, by creating the illusion that the TW does pass so they can live as if no-one knows they’re trans, even when we all do tend to know really.
I think since the cohort of trans people (and the accompanying narrative) has changed so significantly from the days of the GRA (as the SC acknowledged: nowadays, a transwoman with a GRA could potentially be indistinguishable from any other man), it could be argued that a transwoman who doesn’t pass doesn’t actually enjoy the right to privacy around his biological sex anyway, so neither the EA nor the SC ruling has removed the privacy they enjoyed as people can see they are trans anyway as they still live in their male body (and were still socialised as male, which is another glaringly obvious clue for women).
I would also argue that, because trans activism has been so incredibly successful in persuading the general public to treat someone as the sex they’re trying to present as, even when it’s obvious they’re trans, the transwoman himself is actually the least reliable person to know whether they truly pass or not, as everyone around them will lie out of politeness, so the perception they gain from their “lived experience” is actually less valuable than a stranger’s opinion on whether they pass (which would be a horribly inhumane court case which I’m sure no judge would want to touch with a bargepole - it feels more like something RuPaul should judge than the ECtHR).
In any case, a transwoman’s right to privacy can’t possibly trump women’s right to be protected as a class based on biological sex, so where breaching a transwoman’s privacy to confirm his biological sex is necessary to give effect to women’s sex-based rights (which affect far more important areas like safety) then on balance, that privacy breach is obviously a necessary and proportionate one.