AWS Lightsail WordPress – connect to database on instance using mysqli

I have a wordpress website hosted on AWS Lightsail. On that website, I would like to use a shortcode to retrieve data from a database using mysqli. However, everytime the script that connects to the database is executed, I receive a connection error. The database is on the same AWS Lightsail instance.
I was wondering if I need to establish an SSH-tunnel because this is also needed if I connect to phpmyadmin. But since the script is executed on the server itself this does not really makes sense in my understanding. I have used the exact same code on a local host and it worked perfectly fine. What am I missing here?