Is a person considered sinful if they miss Fajr prayer because they relied solely on an alarm clock and did not wake up, despite feeling regret?

You are not sinful for missing Fajr prayer due to being overcome by sleep, because the pen is lifted from the sleeper until he awakens, and negligence occurs only in wakefulness, not in sleep. The expiation for one who forgets a prayer or sleeps through it is to pray it when he remembers it.