* Enable master authorized networks.
Explanation:
Creating GKE private clusters with network proxies for controller access When you create a GKE private cluster with a private cluster controller endpoint, the cluster's controller node is inaccessible from the public internet, but it needs to be accessible for administration. By default, clusters can access the controller through its private endpoint, and authorized networks can be defined within the VPC network. To access the controller from on-premises or another VPC network, however, requires additional steps. This is because the VPC network that hosts the controller is owned by Google and cannot be accessed from resources connected through another VPC network peering connection, Cloud VPN or Cloud Interconnect. https://cloud.google.com/solutions/creating-kubernetes-engine-private-clusters-with-net-proxies

To control internet access on a per-URL basis (including hostname and path), you should deploy Secure Web Proxy with global access enabled. The Secure Web Proxy will allow policy-based filtering of web traffic, allowing control over which URLs can be accessed based on the URL list defined in the policy. Unlike Cloud NAT, which does not support FQDN filtering, Secure Web Proxy is designed to provide such control, especially for scenarios with sensitive or controlled internet access requirements.
Reference: Google Cloud - Secure Web Proxy Overview
Reference: Google Cloud - Setting up URL filtering