I have a friend who studied cognitive science and he says that while there is science to support various theories, the whole “consciousness” thing is very much stuck as metaphysics and philosophy right now. There’s no clear consensus as to what it is or why it happens.

For my conjecture, I’ve always figured that memory is significantly more responsible for our perception of individual personhood than any actual continuity of a single consciousness is. That it’s an emergent property of certain recursive systems. The split brain experiments are pretty eye-opening in that regard