The title is my question. I googled and try something like
mysql> !\\ clear
mysql> !\\ cls
mysql> system cls
mysql> system clear
blah blah ...
You are typing the command wrong. It is "\" before "!" and not after. The command ctrl+L will not work for windows. To clear mysql console screen, type following command.
mysql> \! cls
This will do the job for windows. "\!" is used to execute system shell command. "cls" is command to clear windows command prompt screen. Similarly if you are on linux, you will type "ctrl+L" or following,
mysql> \! clear
source: https://dev.mysql.com/doc/refman/8.0/en/mysql-commands.html