How can one reconcile studying medicine with voluntary acts of worship (Sunnah), such as [reciting] the Qur’an and staying in the mosque after Fajr, while applying the jurisprudence of priorities?

Studying medicine is an act of worship to Allah if you intend to benefit Muslims and fulfill the communal obligation (fard al-kifaya).

Combine different acts of worship by prioritizing the obligatory (fara'id) then the supererogatory (nawafil). Knowledge of this comes through increasing beneficial knowledge.

Combining these duties is achieved by organizing time and not wasting it. Much of what is thought to be impossible is due to wasted time. Strive to invest your time wisely.