Is it permissible for an employee to work overtime at another company, given that they signed a contract with their primary company that stipulates not working with any additional company?

You are obliged to fulfill what you committed to and signed in the employment contract regarding not working with another party, for Allah Almighty says: "O you who have believed, fulfill [all] contracts," and the Prophet, peace and blessings be upon him, said: "Muslims are bound by their stipulations."