Must I confess the truth to the manager about lying about going to the mosque, and bear the consequences of that?

It is obligatory to fulfill the employment contract and adhere to work hours. It is not permissible to leave during working hours for personal errands unless granted permission by the employer, as this is considered deception. Lying is a sin, and one must repent to Allah by abandoning the sin, regretting it, and resolving not to return to it. You are not required to confess the truth to the manager if you fear punishment, but you must repay an amount equivalent to the unauthorized absence period to the institution. If it is a private institution, the payment goes to it; if it is a public one, it goes to the general welfare of Muslims.