In terms of single sex services whatever decison the Scottish Government decides re GRC this will have to operate within the EA UK act. It is this act that allows for the provision of single sex service where deemed necessary.
Not sure if Scotland could resign from the UK EA and create its own.
The reality is that why we have so few genuinely women only services are not because of the existing GRA but because so many who could apply the EA excemption that allows single sex services have failed to do so. Not just women's groups in Scotland but throughout the UK. Neither have prisons, hospitals etc..
Or worse still, thanks to Stonewall brainwashing, many have attempted to present the EA as saying someone with a GRC is a woman for the purposes of single sex provision. Which they clearly aren't which is why there is an excemption. And this excemption actually proves the lie of a GRC because if it genuinely change someone's sex then you wouldn't need the excemption. ie the excemption proves that sex is the biological reality that is confirmed at birth.
Had there been, or there still could be, a campaign to make sure the excemption that allows singe sex services was used on every occasion it could be used, changing how someone obtains a GRC wouldn't be an issue, because for the purposes of the EA they are still the sex they are born.
(The Labour ammendment that was challenged in fact was to confirm that the provisions of the EA would not be changed by any new Scottish GRA. I dont know what happened to it after it was challenged for not being in time or something. Presumably this was Labour's attempt to show they did on one level support women.)