To configure private network for client service you will need to assign some IP addresses to client, either manually or trough automation modules like IP Provisioning.

VLAN Isolation

To make this work you will need to assign client with separate IPAM list, and assign that list with unique VLAN in IPAM.
In your product settings Connect with App > IPAM:

Automation with IP Provisioning

Create new IP Provisioning product and:

In Proxmox Product > Connect with App > Client IPs select your IP Provisioning product.

With this setup clients can purchase IP provisioning services to get private network, you can offer this in a bundle or a subproduct for proxmox services.

Make sure that you do not use the same list that was configured in proxmox IP pool, IP provisioning will split selected list into smaller subnets and assign those to client services.

Bridge Isolation

You will need to prepare your cluster and create multiple network bridges that can later be assigned to clients.
In your product settings Connect with App > Network:

With this setup provisioning will assign unique bridge to client profile, this bridge can then later be selected when creating new network interfaces from client area. Assigned bridge is usable for all client proxmox services.