I finally fixed my Late 2013 MBP, which has been rebooting whenever I log in since a fit of rage during Christmas Break, with an iphone backup and a resulting unintentional upgrade to Big Sur. Safe mode would work. First time login with a new account would work. First time login with a new OS on a new drive would work. Otherwise, about the moment you would expect to see the Finder background, it would restart. I could not find any errors in boot logs. Finally after having it turned off for a couple of weeks, and going back to an older install of Big Sur, I saw something different. A first boot sort of "I'm going to calibrate your battery" and when I clicked OK, it rebooted. Turns out the battery was DEAD. 6% or less charge, and quite swollen. Don't know why I didn't notice that earlier. OS in Safe Mode did not call it a bad battery though, just that it was not charging. Today I replaced the battery, and now it boots fine, logs in fine, reboots when I tell it to reboot. All is good again. So, bad battery = no login, even though it was plugged in.