Does a dream about working in a hospital and treating a cancer patient after performing Istikhara have a connection to Istikhara and its meaning, or is it merely thoughts from the subconscious, especially with a desire to specialize in oncology in the future?

The recommended approach is to consult knowledgeable family members, then perform Istikhara (prayer for guidance) and proceed with the matter. If it is good, Allah will facilitate it, and if not, He will avert it. Dreams can be a source of comfort in Istikhara but are not definitively binding as an indication. You can repeat Istikhara and proceed with the matter. If the impact on studies is unknown, you can try it for a period, and if harm is found, you are free to abandon it.