Well, often you'll find detailed descriptions of the medbay's equipment and layout. Also, interactions between the OC and established characters are common, as well as the OC facing medical challenges and finding unique solutions.
Typically, such fanfics might include the OC's backstory and how it relates to their role in the medbay. There could be moments of tension during medical emergencies and maybe some character development for the OC as they handle difficult situations. Also, the relationship dynamics between the OC and the Doctor could play a significant part.