"Your computer restarted because of a problem" when installing macOS Big Sur in external SSD?
Apparently the Big Sur installer has issues with certain external drives.
I tried installing Big Sur on external flash drives (SanDisk and Samsung), neither a fresh install, nor an update from Catalina worked (resulted in endless reboot loops or kernel panics).
I ended up installing 11.2.3 on an external HDD (from LaCie).
Although I also got a kernel panic on the 2nd reboot that occurs during the install, it rebooted and went on to finish the installation without further issues.
I then used CarbonCopyCloner to clone the HDD onto the flash drive and was successfully able to boot and use the system.
(You might be able to perform the clone with disk utility as well.)