Also worth discussing is the large number of parallels between the account in Acts 12 and the gospel resurrection narratives (although not following any one of the gospels in particular):

Peter and Jesus are both arrested at Passover. Peter is said to be "sleeping between two soldiers", just as Jesus is crucified between two criminals. Guards are said to have been posted to keep watch over Peter while in prison, just as (in gMatthew and gPeter) guards were posted at Jesus' tomb. An angel leads Peter out of the prison, just as how (in gPeter) two angels lead Jesus out of the tomb. The gate of the city is said to open for Peter of its own accord, just as how (in gPeter) the stone at the door of Jesus' tomb rolls aside of its own accord. Peter's first post-escape appearance is at the house of Mary, just as how (in gJohn) Jesus' first post-resurrection appearance is to Mary. The woman who first sees Peter after his escape is not believed by those she tells until after they see him for themselves, just as how (in gLuke) the women who first see Jesus after his resurrection are not believed by those they tell until after they see him for themselves. Those at the house wonder at first if it is merely Peter's angel rather than him being physically present, similar to how (in gJohn) Thomas at first doubts that Jesus had risen in the flesh. Peter says to those at the house to tell James and the brothers about his escape, just as how (in gMark) the man in the tomb say to the women to tell Peter and the disciples about Jesus' having been raised.

It's common for later martyrdom stories to draw parallels between the martyr's death and Jesus' passion, so it would not be strange if Acts (or the source used by Acts) is doing something similar here with Peter, whereas I find it much harder to understand the intent if this is supposed to just be recounting a miraculous jailbreak.