An Aurora database engine (as with every type of database engine in RDS) supports both external and internal variations of databases.
If your database endpoint is public this would have either been selected initial creation, or modified after it had been created.
VPC Endpoints in your context, would be used to connect to the RDS service (interacting with the API via SDK or CLI). Whereas you want to be able to just keep the traffic to your database private.
You can create a VPCLink to a Network Load Balancer to allow limited connectivity to resources, but this would be used to share outside of your VPC.
In Terraform this option is publicly_accessible, which will define whether it is accessible outside the VPC (or its network connections) or not.