Is a person excused if they miss Fajr prayer (or sometimes Dhuhr and Asr) due to prolonged sleep resulting from taking psychiatric medication at night or during the day, and is that considered a sign of Allah's wrath?

The default rule is the obligation to perform prayers at their legally prescribed times, as Allah the Almighty says: (Indeed, prayer has been decreed upon the believers at specified times). However, if delaying the prayer is due to an excuse, such as heavy sleep caused by medication, there is no blame on someone who strove to take the means to wake up but was unable to. In such a case, they must make up the prayer when they wake up, as the Prophet, peace and blessings be upon him, said: (Whoever forgets a prayer or sleeps through it, its expiation is to pray it when he remembers it). It is recommended to take medication at a time that does not conflict with prayer, after consulting a doctor, or to delay sleep until after Fajr, and to combine prayers if possible. Otherwise, missing one prayer is lighter than missing two.