Absence or presence of a penis is a fact. Interpreting that as sign of biological sex is a construct.
Not really. It might conceivably turn out to be wrong, but we're back to reproductive sex again (and no definition of biological sex can avoid reproduction). So if it turns out that the baby with a penis isn't actually developing to reproduce in the 'male' way, it may be that the interpretation of the presence of a penis was wrong, but generally speaking, 'having a penis' is quite a reliable indicator, and sadly if the interpretation is wrong, that's an indication of a developmental disorder.
This is where I do have an issue with some of the language that is coming in for these things - in this instance, 'assigned male/female at birth'. What exactly are we talking about there if not sex? But the word 'assign' has connotations of an active role on the part of the assigner, as if it could have been done differently. So later, you can say 'I was assigned male/female at birth, but I'm not really'. I think that misunderstands what is done at birth tbh, and in many instances, it goes as far as suggesting that it was the gender that was being assigned, or as co-op has been saying, that
sex is the construct and
gender the essential to being, so you can only guess at the essential bit at birth as it only comes out much later.
There is a great deal of muddle over the difference between sex and gender - increasingly so, it seems to me, as I regularly see the word 'gender' used now when what is actually meant is 'sex'. I suspect that people don't really like thinking so hard about it each time so just plump for a default choice, which used to be 'sex' and is now 'gender'. But I see people getting it wrong who really shouldn't be getting it wrong, including science writers. We're in danger here of replacing the old obnoxious, and mostly wrong, sex essentialism with an equally objectionable, and wrong, gender essentialism.