There's no one thing that defines sex, that's what makes it so complicated. What is often thought of as "biological sex" are two clustered sets of checkboxes (e.g chromosomes, genitalia, secondary sex characteristics, primary sex hormone), but people often have a mixture from both lists. Here's an interesting nature article on it https://www.nature.com/articles/518288a

To preface: this is from a previous bout of hyper focus curiosity (i.e. I am not an expert). But the human genome is significantly more complex than "XX chromosome means biological female". Other genomic markers can trigger that don't align with the typical, which can result in male reproductive organs on a person with XX chromosome and vice versa. XX and XY are also not the only options. There are three, four, and even five somal groupings (e.g. XXY, XYY, XXX - note that to my understanding, you can't have all Y chromosomes even in these outliers). If anyone has further information or any corrections for me, I'd welcome them - I'm going off of memory from a couple of years ago and it's not directly relevant to me (i.e. I am cis-male with no known chromosomal abnormalities)