Yes you can read it that way but only if you understand gender and sex to be different things. The question is whether the labour party consider gender and sex to be interchangeable linguistically....
No. The manifesto is clear. I understand your levels of distrust but don't let them blind you.
The single sex exemptions are limitations to the entitlements conferred by a GRC. Labour is promising to a) retain them and b) encourage use of them by services and organisations.
At the same time, they are promising to make it easier to get a GRC.
These two things are not incompatible at all.
It's not a fudge or a lie about language. It's a genuine concession to women. Does it go far enough to earn them a vote from me? No. But it may be for some.