This question would probably be better suited for a recommendation thread, as this one is more about identifying games that forum users recall but can’t find, but to the best of my recollection,
Aegis Project and Thousand Miles of Sky are WIPs that both let the player set skin tone, although there isn’t an option to set a specific ethnicity.
Gilded Rails and Tin Star are the only published games I know of that let the player set ethnicity specifically, although neither game covers every option. There’s a pretty decent chance there are more that I haven’t played, though