”Trans race" and "trans age" are red herrings. Your race is defined by your ancestry, your age by chronology, but sex is much more complex and can be defined in various ways from gametes to gender identity and can vary by context.
I feel it’s important to point out that race is not defined by ancestry. Race is much more of a social construct than sex is. In many ways, race is to ancestry as gender is to sex. It is externally applied to people - often regardless of their actual ancestry. For example In the US for a long time if someone has even one great grandparent who was Black they were legally considered Black (one drop rule). This comes from the fact originally that slave owners wanted to be able to continue to enslave the children of rape on their plantations. We have since moved to self identity of race, which I think is appropriate given even ancestry - let alone race - truly can be a spectrum (unlike sex, see below).
All that to say - claims that “race” is more biologically real than sex are verging on race science / scientific racism. You should be more careful.
Biological Sex on the other hand really is defined by gamete production. Just to clarify:
In anisogamous, dioecious species like humans, two gametes must fuse to produce offspring. Two body plans exist in all such species to produce the two gametes and get them together and grow to produce a new individual. Individuals that produce neither gamete are not a cohesive third category because they include people with an array of simple and complex medical conditions, juveniles, and post menopausal females. None of this is controversial. However none of this in my opinion really helps us answer the question at hand so it’s a bit of a pointless exercise.
The question at hand is should the law recognize the category of people who are presumed to produce large gametes, or should they recognize the category of people who claim to be women? Should both be recognized? One or the other?
I’m open to the idea of both but that requires that distinctions be made to categorize people by BOTH biological sex and gender identity and trans activists in particular seem to be unwilling to accept this to any extent. Feminists in turn have become more hardened against this approach as well.