This case is actually another nice example of the difference between biological reality, and social relations. So, just as being male or female (sex) is a biological fact, but someone may want to be treated as a masculine or feminine person by society (gender), so we need the amended birth certificate of the GRC (but still kept on record elsewhere that this has been done). So, for social reasons, you can get a birth certificate that accords with your presented gender.
But in this case, the amendment would not be for the benefit of the person for whom the certificate is issued. There is no procedure in place for you to change the birth certificates of someone you give birth to. If it were allowed, it deprives the child of correct factual knowledge about their parentage. Just as if a transwoman who fathered a child wanted to refuse to be named on that childs birth certificate because by so doing that would out them as male. Well, in that case I would say, if you didn't want to be outed as male, you shouldn't go around fertilising eggs with your sperm.
A child, however produced/adopted/whatever, I think has a right to be able to access their biological origins, however uncomfortable fathers and mothers may get (one reason why so hard to get sperm donors nowadays). So, the biological relationship is what it is, even if you want to have the 'social' relationship to a child as a 'father', and even if you might someday have to deal with explaining the complications.
I suppose, as regards the child, the closest comparisons are like cases where a child later discovers that then person they thought was their mother was actually their grandmother, and their supposed sister was actually their mother. These situations, although easier for the adults concerned are not always easiest for the child, who has a right to know where they came from if they want, however complicated or convoluted.