Our standard cPanel shared and reseller plans are built around MySQL/MariaDB, which covers WordPress, Laravel, Joomla, and the vast majority of web apps. Some cPanel servers include PostgreSQL Databases as well, but availability varies by server.
To check your account, log in to cPanel from your client area and look for a PostgreSQL Databases icon in the Databases section. If it is present, you create databases and users there much like MySQL.
If you specifically need PostgreSQL and do not see it, a VPS or dedicated server lets you install and configure any database engine you want. Open a ticket to confirm options for your plan.