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As mentioned in this document under limitation section converting an existing AKS cluster to private one is not supported. Private AKS cluster does not remove the Public IP address from the data plane load balancer. Only API server to data plane communication happens over private link.
For your case, Pods does not have public IP Address. Looks like you are using Public Load Balancer type Services.
You can try switching to use an ingress controller which will have one frontend public IP address associated on the Azure LB and configure different paths to route requests to your services internally from the ingress.
Ref: https://learn.microsoft.com/en-us/azure/aks/ingress-internal-ip?tabs=azure-cli#create-an-ingress-controller
If you don't need Public Connection to the AKS Services at all then you can switch to internal load balancer type service.
Hope this helps.
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