Most of the default installations of Nextcloud goes with MySQL/MariaDB, but Nextcloud support other databases too like PostgreSQL and SQLite. I will show you how to install Nextcloud with PostgreSQL on Ubuntu 22.04 in this article with Apache and PHP.
I would not go into details of what is PostgreSQL as I am pretty sure you already know about it. But in this guide, we will install and use PostgreSQL in Arch or Manjaro operating system with PHP including how to manage the databases.
OpenProject is another web based project management tool written in Ruby and Angular available under GPLv3 license. If you want to give it a try and know what it offer, follow this article to setup OpenProject on Ubuntu 20.04.