Our requirement is to follow Google recommended practices to achieve the end result. Configuring Private Google Access for On-Premises Hosts is best achieved by VPN/Interconnect + Advertise Routes + Use restricted Google IP Range.
Using Cloud VPN or Interconnect, create a tunnel to a VPC in GCP
Using Cloud Router to create a custom route advertisement for 199.36.153.4/30. Announce that network to your on-premises network through the VPN tunnel.
In your on-premises network, configure your DNS server to resolve *.googleapis.com as a CNAME to restricted.googleapis.com is the right answer right, and it is what Google recommends.
Ref: https://cloud.google.com/vpc/docs/configure-private-google-access-hybrid You must configure routes so that Google API traffic is forwarded through your Cloud VPN or Cloud Interconnect connection, firewall rules on your on-premises firewall to allow the outgoing traffic, and DNS so that traffic to Google APIs resolves to the IP range youve added to your routes.
You can use Cloud Router Custom Route Advertisement to announce the Restricted Google APIs IP addresses through Cloud Router to your on-premises network. The Restricted Google APIs IP range is
199.36.153.4/30. While this is technically a public IP range, Google does not announce it publicly. This IP range is only accessible to hosts that can reach your Google Cloud projects through internal IP ranges, such as through a Cloud VPN or Cloud Interconnect connection. Without having a public IP address or access to the internet, the only way you could connect to cloud storage is if you have an internal route to it.
So Negotiate with the security team to be able to give public IP addresses to the servers is not right. Following Google recommended practices is synonymous with using Googles services (Not quite, but it is at least for the exam !!).
So In this VPC, create a Compute Engine instance and install the Squid proxy server on this instance is not right.
Migrating the VM to Compute Engine is a bit drastic when Google says it is perfectly fine to have Hybrid Connectivity architectures https://cloud.google.com/hybrid-connectivity.
So,
Use Migrate for Compute Engine (formerly known as Velostrata) to migrate these servers to Compute Engine is not right.

Cloud Functions is Google Cloud's event-driven serverless compute platform that lets you run your code locally or in the cloud without having to provision servers. Cloud Functions scales up or down, so you pay only for compute resources you use. Cloud Functions have excellent integration with Cloud Pub/Sub, lets you scale down to zero and is recommended by Google as the ideal serverless platform to use when dependent on Cloud Pub/Sub.
"If you're building a simple API (a small set of functions to be accessed via HTTP or Cloud Pub/Sub), we recommend using Cloud Functions." Ref: https://cloud.google.com/serverless-options

Using primitive roles The following table lists the primitive roles that you can grant to access a project, the description of what the role does, and the permissions bundled within that role. Avoid using primitive roles except when absolutely necessary. These roles are very powerful, and include a large number of permissions across all Google Cloud services. For more details on when you should use primitive roles, see the Identity and Access Management FAQ. IAM predefined roles are much more granular, and allow you to carefully manage the set of permissions that your users have access to. See Understanding Roles for a list of roles that can be granted at the project level. Creating custom roles can further increase the control you have over user permissions. https://cloud.google.com/resource-manager/docs/access-control-proj#using_primitive_roles
https://cloud.google.com/iam/docs/understanding-custom-roles

Authorizing with a service account
gcloud auth activate-service-account authorizes access using a service account. As with gcloud init and gcloud auth login, this command saves the service account credentials to the local system on successful completion and sets the specified account as the active account in your Cloud SDK configuration.
https://cloud.google.com/sdk/docs/authorizing#authorizing_with_a_service_account