This question should be answered based on Advaitha only.
There are many jivan mukthas across scriptures who carried out their profession: Rama, Krishna, Vasishta, Vyasa, Suka, Vishwamitra, Lila, Prahladha, cudala and many others.
It is true that a person who is Jivan muktha is parabrahman herself.
So, she has the faculty of satya samkalpa i.e., whatever she thinks or desires to do will become true.
Suppose a jivan muktha is a queen of a kingdom. Then, she need to perform a lot of tasks such as safeguarding good people, punishing thieves, propagating knowledge etc., for the sake of dharma.
Then why do jivan mukthas, who are continuing in professions, across scriptures won't use the faculty of satya samkalpa without any physical effort for their profession?
As a side note, I want to mention the fact that all people do their dharmas with mental effort only in Krita yuga.