Hello,
Considering the type of error you are receiving, it would be my recommendation to follow the troubleshooting steps on the GKE troubleshooting in here.
If the issue persists we can attempt the following as well:
-Verify scopes/permissions for your cluster by navigating from GCP>KE> Cluster>permissions> Cloud SQL should be “Enabled”.
(Note: if you see Cloud SQL: Disabled then you can enable the API permission here.)
-You had mentioned that a docker image was built exposing port:5432. I would like to inform you that only your proxy port should be set to 5432.
(Note: When a cluster is created the default port for the proxy is 5432. Connection errors can occur if the same port is used for both the cluster and your proxy within the pod.)