The problem with saying 'women and pregnant people' is that it creates ambiguity.
First of all, woman is the sexed noun we have for an adult human female.
"People" is a sex neutral term for humans, (adults and children also sex-neutral) of any age.
So saying 'women and birthing people', are they saying that others besides the sexually mature females are giving birth? Common sense would say 'no' because males of any age and females who are not yet sexually mature or females beyond menopause do not give birth.
The other possibility is that 'women' and 'birthing people' are being used in the gendered (Queer theory) sense of the words. And reproduction is a sexed activity, not a gendered one.
But if you want to pretend that genders give birth then that raises another bunch of ambiguity.
Except QT adherents say that 'not only women give birth' meaning who? Does this then include trans women? Because, you know, TWAW. But we know that males who identify as trans do not have the capacity to give birth and trans men actually have the capacity to give birth yet, TWAM. But is trans men are 'men' and men don't give birth... I don't know, it is a muddle.
Then what is the purpose of saying 'birthing people' who are they? Toddlers, grandads? Great aunt Effie? Are they trans men? Then why not say women and trans men? Then why not say trans men then?
Finally, are they using 'women' in a sexed way and 'birthing people' in a gendered way? Documents in maternity care is once more dealing with a sexed activity and sex takes priority over gender for the vast majority of service users.
While trans identifying females need to have specialist attentions from care teams looking after them, the majority of their care falls under the same procedures of the rest of women and the care teams pick up the specialist issues they present on an individual basis.
Why are the specialist care they deserve not being dealt with on a case to case basis as needed instead of it rising to the status on par with the rest of the woman-centred care they deserve?
No general policy statements include care for 'women and women who were raped' care protocols or 'women and women who live with disability' or women and women who experience drug abuse, domestic violence, and so on repeated ad nauseum because 'women' serves them all. They have also deserve to have their specialist care plans but the vast part of their care is done within the services that all women deserve. Similarly trans men are another demographic of woman.
Feelings are not the centre of policy documents and press releases. Clarity and relevance are.