Macbook keeps restarting during big sur update

I would leave it for a bit longer then, and let the update continue for as long as it needs to. I’m not sure what your time zone is, but let it continue overnight if possible. If it’s not done in the morning, that would indicate that something is not working as expected.

It’s pretty normal for the screen to go dark and turn back on during the update. How long has this been going on for?

Does it ever show a progress bar/ Apple logo?

No problem! Hopefully everything goes well 👍