Connection timeout error from Local to AWS Mysql & Postgres databases

Hello.

Public accessibility must be enabled in RDS for direct access from local clients.
https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/infrastructure-security.html#infrastructure-security.publicly-accessible

After enabling public accessibility you need to configure the RDS security group's inbound rules to allow your IP address.
https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/Overview.RDSSecurityGroups.html

Also, make sure that the subnet specified in the RDS subnet group is a public subnet.
If this is a private subnet, you will not be able to connect to it even if public accessibility is enabled.
https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_VPC.WorkingWithRDSInstanceinaVPC.html#USER_VPC.Subnets

Since it is not recommended to make RDS publicly accessible for security reasons, please also consider the connection method described in the following document.
https://aws.amazon.com/jp/blogs/mt/use-port-forwarding-in-aws-systems-manager-session-manager-to-connect-to-remote-hosts/