Is it considered disbelief to delay the Fajr prayer until after sunrise, knowing that I woke up to the adhan, intended to sleep a little longer, and then was overcome by sleep until sunrise?

Scholars have differed on the ruling concerning one who intentionally abandons prayer. What occurred with you does not fall under this issue, as you did not intentionally delay the prayer beyond its time. Although you erred by delaying the prayer, if you thought you would wake up before the time expired, we hope no sin befalls you. However, if you knew you would not wake up until after the time had expired, then you have sinned thereby, and you must repent. It was incumbent upon you to hasten to perform the prayer once you woke up after sunrise, because many scholars hold that making up a prayer must be done immediately. Although many of them also hold that making up a prayer can be done at leisure if the delay was unintentional, and according to this opinion, there is no sin upon you.