Thank you both for your replies.
I managed to complete the installation (run also apt full-upgrade successfully) and then reboot.
After the update the system boots only with the ttys (1-6) and not with a graphical interface, and by that I mean that I tried to change to the graphical interface with Ctrl-Alt-F7 and Ctrl-Alt-F8.
I verified that Debian 10.10 was installed , ran cleaning commands, reboot again but again I can only access ttys and not the Graphical Interface.
Is there any possibility that a graphical environment has not been installed at all?
All the update procedures that I have seen, do not have extra steps. What am I missing?