Just restoring the database to a different server doesn’t mean you are setup for remote connections on the mysql side. While I don’t use easyengine with a remote database again that defeats the purpose of this project. I can tell you when I have a working site in ee4 and I change the /opt/easyengine/sites/example.com/app/wp-config.php DB_HOST variable, I see an immediate change of the site going from working to not working. That tells me the site is pulling the server name from there. Have you made a successful remote connection to your mysql database using an outside machine? Attempt to connect directly from a mac workstation using Sequel Pro, the mysql command line from a Linux machine or another server, or the GUI / front-end tool of your choice on Windows.
https://support.rackspace.com/how-to/mysql-connect-to-your-database-remotely/