That is the crux of the issue - I can understand when a married couple (male + female, the only legitimate kind of marriage) has fertility issues - like the prospective father is sterile, pursuing sperm donation, though adoption would be a far more God-glorifying and society-helpful avenue to children.
But when single women or homosexuals decide to circumvent God’s pattern and purpose - they are sinning and I have zero sympathy for that person and there rebellion.
As to the child - I see no legal obstacle to her seeking knowledge of her donor father once she is of the age of “majority” - but mom signed a contract and then tried to break it.
Possible that mom’s secret fantasy was the donor would show an interest in the kid and then the mom with the end result of everyone living happily ever after as a family.