Some others have reported issues like this. Here is something you can try that worked for me with an earlier OS where I experienced something similar. *This only works if you have a reliable backup you can restore from.*
(1) Boot into recovery and erase the hard drive, then reinstall the operating system. (You may have done this already, but you did not indicate if you erased the disk first. *Only do this if you have a reliable backup to restore from.*)
(2) You now have a fresh operating system with no user files and no user-installed programs or extensions. Basically like the way a new computer comes. On first boot, create a new user, ADMIN, who has Administrator privileges. Don't migrate your user accounts or files over from your backup yet.
(3) With this plain vanilla system and the single Administrator user, apply all the available updates, including the troublesome Security Update.
(4) So far, this should work just as it does with new Macs in the Apple Store. Assuming it does work, then run the Migration program to migrate your user accounts and files from the backup. I suggest not bringing over software or settings, you can pick what to migrate, I suggest just user accounts and files, but no programs or settings. Then install fresh all your software, but either one at a time or a few at a time. Reboot to verify that you can restart your computer properly after each install. If one of your programs causes the reboot stoppage to return, then that program has a conflict with this latest version of Catalina.
This approach takes a while longer because you are reinstalling all your third party programs from scratch, and you also have to reinstall printers, scanners, and re-enter settings such as for routers, etc. You'll need registration numbers, etc. But it will work if there was something previously installed that was conflicting with the most up to date version of Catalina.
If this fails at step 3, then that might be indicative of a hardware problem.
