After multiple attempts of trying to fix CLIENT_UNAUTHORIZED  within Amazon Lightsail SSH console. I finally succeed. Still not 100% sure how. Why? Because what I did for one server didn’t seem to work on the other.
Updating my first Debian server I could have sworn I selected maintainers version of openssh server configuration file. But when updating second Debian server this definitively caused CLIENT_UNAUTHORIZED  error to reappear after updating. Only when I selected currently installed version – did second server update without an error when trying to log into Lightsail SSH control console.
On each server I did this step.
sudo nano /etc/ssh/sshd_config
Add following 2 lines to /etc/ssh/sshd_config
And then these instructions
sudo apt-get remove openssh-client openssh-server
sudo apt-get install openssh-client openssh-server
Previously doing those steps had not resolved problem. I can only assume I must have selected maintainers version of file. Assuming that might be a more secure option versus possible modified file within server.
Using steps above and selecting currently installed version of openssh server configuration file – I no longer had an error when logging into console after update.
Both servers are now backed up in Amazon Lightsail Instance after I confirmed several times that console was working properly.
That website and others were linked in my previous articles.