Why has it all been done quietly by the backdoor?
Because it is perfectly well known that it cannot be achieved by fair means, in full sight, with full informed consent of the electorate.
Which admits, there's no mandate, it would raise protests and questions that couldn't be overcome, and it cannot stand on its own merits. It requires the subjugation of all female people's needs and feelings and best interests to those of a tiny percentage of those born male. It is fundamentally unfair and unjust and unequal. It cannot allow equal consideration to be given to those born female because if that is allowed to happen it does not work.
The hope is that if it's made law it will just be impossible to undo and female people will shut up, go away and eventually get used to their subordinated, lesser position and losses as the new normal.
One would hope that parliament and MPs would get a bit more interested in the ethics of a political lobby group being enabled to reframe, adapt and alter laws in their own best interests against the decisions of the HoC and due process. Because if that's how things are going to work and that's ok, why bother with MPs or the HoC at all? Why bother with the Civil Service and equality law at all when it just says what the most powerful political lobby group want, regardless of things like fairness, equality, consideration of all tax payer interests etc?
No taxation without representation. Dig. Yes. And if this finds in the favour of said political lobby group it will lay out before the electorate in clear sight: females are second class citizens in the UK, subordinate at all times to the best interests of males. And MPs/HoC are just expensive noise makers, the law is made by stealth with no regard for democracy or the very expensive piles upon piles of law and legislation the HoC roll out.
Good luck getting that past the UK general public. Boris is already clear that this whole situation is a poison chalice.