I have seen birth father used in this context. Obviously, it may end up not being the best term in the long term due to the confusion you mentioned.

But, you do realize that a surprising number of people have a mismatch between their genetic sex and their phenotypical sex, and we don’t even know how many because we typically only find it when they are checked after demonstrating fertility problems. Some XY females and XX males have symptoms, some don’t. I’ve never had my sex chromosomes checked, so for ALL I know I have a Y chromosome, and I’m a cis woman.

Hormones are what determine sexual phenotype, not genetics. You can have two X chromosomes but have SRY transcription (SRY is the specific gene that triggers elevated testosterone levels) and develop as a phenotypical male. You can have a Y chromosome but have androgen insensitivity and develop as a phenotypical female. You can have a Y chromosome that has lost the SRY gene…

It’s a lot more complicated than what we learned in high school.