This is certainly going to be very tin-hattery, but I see a big connection between changing the diagnosis of sexual dysphoria from a mental health condition to a physical one and the change to self-ID.
Mental health conditions are notoriously hard to treat and expensive and lock people into a life time of talking therapies. The NHS can't afford it.
A physical problem that affects lots of different people (not just those with dysphoria - with the umbrella now including lots of different conditions) means that pharmaceutical companies can get in on the act. it brings money into the picture.
I really think that the government supports this because they have "seen the money" and drugs and surgery is an industry - while one to one sessions with a therapist is not. The government can bring in self ID and wash their hands of people with dysphoria - passing them over to drugs companies.