Same problem here with iPad Pro after updating from 14.8 to 15 official release. As soon as I would enter my password to unlock after the upgrade, it would loop a couple of times, flashing the time on the screen between each loop. After about 5 loops it would then restart. I really wasn’t keen on having to remote erase or do the recovery mode restore. Not at all how I wanted to start my morning. I was able to get mine working pretty simply in the end. After it had gone through another one of its looping and restart cycles, and when sitting at the welcome screen (where it cycles through languages, and before attempting to enter password to unlock) All I did was press and release the Volume up then Volume down buttons, then press and hold the Sleep/Wake button - the option to Power Off came up pretty quickly. I powered it off, started the iPad up again and it came back up and loaded correctly. Took me straight to the Your IPad Has Been Updated msg and was able to go on happily from that point on. IPadOS 15 loaded correctly and all is working as it should be. I may have just been lucky. My solution may only work on the 2018 IPad Pro. I’ll try upgrading my iPad Mini 4 next and see. But it’s definitely worth giving it ago before attempting a remote erase or doing the recovery mode restore options.