You seem to be very focussed on Stonewall. Is there a reason for that?
I think they may have scored an own goal where parts of the membership have forced adoption of a policy other parts of the organisation are much more cautious about. Albeit other forces are at work the policy of self ID had seriously damaged Stonewall's reputation for and marketability as a trainer in diversity.
Any change to the law in England would surely start with some form of options exercise followed up by a policy paper. Traditionally white and green papers.
The consultation done in 2018 stated explicitly that the protections in the Equality Act would remain:
https://assets.publishing.service.g...hment_data/file/721642/GEO-LGBT-factsheet.pdf
Why would something far more radical from Stonewall take precedence now?
As to the phrase living in the acquired gender I'm sure there's plenty of explanation in guidance for those applying for a GRC and, further cack when the bill was in parliament. To me it has the ordinary meaning of using the pronouns/names of the acquired gender.
As I've already said I don't doubt there are men (mostly) who might want to enter women only spaces for 'kicks'. I don't think waving a statutory declaration will be a magic wand stopping them from being removed and charged with various statutory or common law offences.
I don't know if there is anything comparable in female changing areas but it's fairly common in male facilities for there to be signs warning against any form of sexualised behaviour. If you're caught
in flagrante delicto whether solo or en masse you'll be out.
I'm not saying men making a nuisance of them selves won't happen; it does now and will in future.
It can though be dealt with proportionately way short of forcing transwomen to ID themselves and shuffle off to some 'third sex' annexe.