According to the episode "Timeless Children," the source of Time Lord regeneration
is genetic, derived from the regeneration abilities of the Timeless Child, who is in the reality the Doctor.
Obviously, this explanation is a lot of new information, but given the mystery previously surrounding the origin of the Time Lords, it would not seem to contradict anything.
However, several seasons back, Amy and Rory's child, River Song, became effectively part-Time Lord due to have being conceived in the Time Vortex. This suggests that the Time Vortex is largely responsible for regeneration.
I know better than to expect complete consistency from Doctor Who, but how are these two things reconciled?