Following the guide at https://cloud.google.com/vpc/docs/configure-private-services-access , I managed to create a private service access connection. However, the second time around (after deleting the existing ones), I'm getting a cryptic error which I'm unable to find a reference to anywhere. Here's the error:
Cannot modify reserved ranges in CreateConnection. Please use UpdateConnection.
The error you are experiencing is expected as currently it's not possible to modify the range you reserved after it is created. This is collected on the GCP official documentation:
After you have established a private services access connection, and created a Cloud SQL instance with private IP configured for that connection, the corresponding (internal) subnet and range used by the Cloud SQL service cannot be modified or deleted. This is true even if you delete the peering and your IP range.
There is a current public Feature Request for this since more users reported the same.
By now, current "solution" is to create another VPC for this as you did.