Why is mangosteen so slow to bear fruit and how long does it really take?

Mangosteen is famous for being slow, and that is just the nature of the tree, not something you did wrong. It is usually grown from seed because grafting is difficult, and seedling trees have a long juvenile period before first fruit, often many years, commonly reported in the range of around eight years or even more depending on care and conditions, after which yield builds up gradually. There is no quick trick to force it; good steady care, shade when young, fertile soil and never letting it suffer drought stress help it grow as fast as it can. Because of this long wait you carry the orchard cost for many years with no income, so plan your finances accordingly and intercrop with shorter term crops to earn in the meantime if your spacing allows. Treat the bearing age as a wide range and confirm what growers in your belt actually experience, since local conditions change it a lot.