Hi.
I am having a similar issue. Macbook pro 13" with retina display late 2013 - upgraded from El Capitan to Big Sur on the day it was released...had download interruptions > restarted > black screen for hours at 12 min remaining mark > turned off and turned on > installation continued > and eventually got completed and I was able to login. However I was presented with a black screen at boot right after first restart. (I had windows 10 installed via boot camp too). Tried smc reset, recovery mode, PRAM reset several times, nothing worked. Called up apple support with whome SMC reset seemed to work. But the behavior remained erratic and unpredictable. Mac would boot to black screen 7 out of 10 times - and will boot successfully randomly. I tried reinstall - same issue - did clean install after erasing disk volumes and containers (clean slate including reformatting OS X Extended format to the new APS format) - same issue - tried recovery mode reinstall - same behavior - tried internet recovery model reinstall - same behavior.
I finally decided to go back to the original OS that came with my mac using the specific recovery mode startup key combination and it did reinstall MAC OS Mevericks but went through similar cycle (black screen during install forcing me to turn off and on), was eventually able to complete installation. But unfortunately, the behavior remains the same... if I restart the machine 10 times, it will successfully boot perhaps 5 out of 10 times - and rest of the times will go to black screen. Similar behavior when using SHUT DOWN option.
The diagnostic option (pressing and holding D while starting) shows no error. Have run disk utility multiple times with no issues reported in start up disk.
Given I have tried clean install multiple times, with and without wipe cleaning disk and have now even gone back to Mavericks, I think something during the update of Big Sur has caused a permanent damage to macbook hardware causing this unpredictable behavior. I have scheduled an appointment with apple authorized repair shop - lets see what they tell me but I am unwilling to pay for the repair as it has been caused purely by the big-sur update.
For all folks having the black screen at boot issue, especially the ones with late 2013 model, I suggest keep retrying the key combinations at the startup even if it does not work, because if what I have faced is a wide spread issue, one particular try would probably bring the mac back to life, but unfortunately, only temporarily. So a permanent fix (after a proper diagnosis) will still be required.