Cannot connect remotely to serverless Aurora MySQL

I have recently created a serverless Aurora MySQL DB in our account. I am attempting to connect to it remotely via mysql-workbench in order to setup the schema, etc. However, I cannot seem to establish the connection. As this document (https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/CHAP_GettingStarted.CreatingConnecting.MySQL.html ) recommends connecting via mysql command line following creation, I assume either command line or mysql-workbench are the recommended/common approaches.

I am attempting to follow the steps under the 'A DB Instance in a VPC Accessed by a Client Application Through the Internet' section of this document: https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_VPC.Scenarios.html#USER_VPC.Scenario4

The associate Aurora security group appears to allow the 3306 port through, but I am still unable to connect: Your connection attempt failed...

What am I missing to allow these connections please?