If you have a server such as a Web Server built using Laravel Forge, it only installs PHP and NGINX.

You plan on using a managed database from Digital Ocean and use the server to run mysqldump for database backup, you will not be able to.

In order to use mysqldump mysql-client must be installed on the server.

Log into SSH and run

sudo apt update
sudo apt install mysql-client

Found info at https://mysqldump.guru/how-to-install-and-run-mysqldump.html