How to disable release upgrade notification at terminal/TTY login (not the GUI pop-up)?

That output is part of the MOTD. To disable it, remove the execute permissions for /etc/update-motd.d/90-updates-available.

sudo chmod -x /etc/update-motd.d/90-updates-available

The output maybe cached for a while, it may take a few login attempts for the message to clear out.

Do this:

sudo chmod -x /etc/update-motd.d/91-release-upgrade

This only removes the message about a release upgrade. It keeps the message about package updates, including security updates, which I would like to keep getting.