Are eunuchs trans?

In my last post I asked about how we as trans people can be certain that God is accepting of our transitions. A few times I saw eunuchs being mentioned so I looked into who eunuchs were, and what role the served. It seems like they fall into one of three categories. Eunuchs who were often castrated so they could serve in a royal court, eunuchs who were born without the ability/desire to reproduce, and eunuchs who chose to be castrated in order to better serve the Lord. While it's not a sin to be a eunuch I think the context matters here. In Matthew 19:12 Jesus references them directly and in the context of marriage. It seems that he's saying it's fine for these people to be this way because marriage is completely optional. In Esther 4:4 the writer seems to draw a distinction between the women and the eunuchs in Esther's court implying that these two groups have different gender identities. So am I misinterpreting scripture here? How do eunuchs and trans people correlate?