MoreCrack.... well, oh crumbs, how can I explain this?
In terms of British law, I am female because my birth certificate says so, and my birth certificate is a legal document of identity that cascades through my life.
All that matters in law in this specific regard is the legal identity of Man or Woman, Male or Female. This legal identity is now termed "gender" and is no longer dependent on biological sex (XX or XY chromosomes, or genital presentation).
The confusion comes because British legislation has confused the term "gender" with the term "sex", so, legally, changing gender now changes "sex".
The safeguarding of individuals who believe they have GD when, in fact, they may not is the two years of living as the acquired gender and a statement of GD. It is not particularly easy to get a GD statement in the UK, but the approach to the issue tends to be that .. well, modern medicine is pretty much about pathology and surgical or pharmaceutical solutions to pathology. The approach is that GD can be "cured" by surgery or pharmaceuticals, such as hormone therapy etc.
"If a person 'lives as' the other sex for 2 years they can change a statement of biological fact?"
Well, your legal identity is no longer a statement of biological fact. Legal gender and "sex" is no longer dependent on biological fact. You can be legally female, and have "a pillar and two stones".
"And actually, this seems to indicate that the right of a person to choose the biological sex of their partner is removed, as long as that partner has obtained a gender recognition certificate...regardless of their possession of the reproductive system of their 'previous' sex."
This is where that confusing section of the GRA comes into play. The CPS states that trans identity does not convey protection from charges of sexual assault or rape, but under the Equalities Act, you are not required to disclose your transgender status.
I would argue if your legal identity is female, but you were born biologically male, you have an obligation to inform a sexual partner in terms of validating their consent to sexual activity. This would fall under "conditional consent".
However, I don't know of a case in Britain where this has been tested under these specific terms. In the McNally case, and the situation in the OP, the circumstances were more straight-forward because the individuals were/will be still legally female. There have been another few cases (Wilson; Barker) where this has also been the case.
Incidentally, you are not legally obliged to tell a sexual partner you have HIV, but if you fail to do so, you can be prosecuted for intentional or reckless transmission if they become infected. It is a bit like, well, you don't have to, but if something goes wrong, you will be prosecuted.
"As far as public records are concerned, their education and salary would be recorded as say, a woman, when they are in fact biologically male?"
Yes. Any crimes they commit will be recorded under female statistics. Any recording of health services they access will be under female statistics. Any interaction with state agencies will be as a woman. Legally, that is what they are.
Incidentally, there was a very interesting quirk after the GRA and before The Marriage (same sex couples) Act because a marriage could not automatically convert into a civil partnership, and same-sex marriage did not then legally exist. If you were married and wanted to change gender, you had to divorce or annul your marriage because marriage was, in legal terms, between a legal male and a legal female. If one of you changed gender to be a legal female, then your marriage would be between two legal females -- and government was not prepared to legally recognise that.