These steps should work for you on Ubuntu 22.04, so double-check the MySQL section.
sudo apt update && sudo apt upgrade --yes
sudo apt install mysql-server --yes
sudo systemctl start mysql.service
sudo mysql
ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'root-password';
QUIT;
sudo mysql_secure_installation
sudo mysql -u root -p
CREATE USER 'user_site'@'localhost' IDENTIFIED BY 'site-password';
CREATE DATABASE site_prod;
GRANT ALL PRIVILEGES ON site_prod.* TO 'user_site'@'localhost';
FLUSH PRIVILEGES;
QUIT;
curl -sL https://deb.nodesource.com/setup_16.x | sudo -E bash
sudo apt install nodejs --yes
sudo npm install ghost-cli@latest -g
sudo mkdir -p /var/www/ghost-site
sudo chown ghost-user:ghost-user /var/www/ghost-site
sudo chmod 775 /var/www/ghost-site
cd /var/www/ghost-site
ghost install