Is it permissible to work overtime elsewhere without the university's knowledge, given that the employment contract stipulates otherwise, and this work does not affect official working hours?

Fulfilling a contract is obligatory, as Allah Almighty says: (O you who have believed, fulfill [all] contracts). If a condition is unrelated to the work, such as stipulating that one may not work outside of official hours in an external job that does not affect the contracted work, then this condition is void because it is not related to the rights of the contract. The Sharia has invalidated every condition of this nature, as the Prophet (peace be upon him) said: "What is wrong with people who stipulate conditions that are not in the Book of Allah? Whoever stipulates a condition that is not in the Book of Allah, it is void." A government or private employee is a special wage-earner restricted by time. When working hours end, the wage-earner is free to dispose of their time and effort as they wish.