I think there are three things in play.
First thing - safeguarding.
An abusive then absent father.
Access - and now unsupervised - beginning again, where he 'seems' to be behaving with his OH.
Behaviour noticeably worse since his unsupervised access started.
Saying things a seven year old should have no concept of - Swearing, insults, threats to harm the baby, self harm, make accusations against your partner, wishing you dead.
Where on earth are these coming from?
Is the significant difference/influence … her father's access to her?
What do you know of his partner?
Second thing - neurodiversity.
You've noticed a tendancy always having been there, getting worse as she gets older (and likely to soar at adolescence), screaming, refusing, running away, difficulty making friends, difficulty learning.
It looks like there are complex neurodiversity issues, maybe learning difficulties also in play.
She needs expert help and support and she cannot get that from either parent or the school.
You shouldn't have to, but being the noisy demanding one may be the only option. There are practical suggestions on the thread to follow there.
Third thing - this is a little girl, a little brain and mind trying to cope with huge adult things.
No father, then suddenly a father who's also got a partner, and a 'step' father.
Mother's attention divided - did the new baby's arrival happen to coincide with father's new access, and less time with you?
Does she feel replaced by another girl with a present dad?
Are you a loving threesome - with your daughter the awkward extra?
Does she feel threatened, endangered by the baby?
Does she have no real security about where she belongs?
Poor love.
And your poor partner - it must be awful and frightening for him, too.