A private cluster cannot be accessed outside of that VNET were AKS cluster was created.
Can you try accessing the private AKS cluster by creating a test VM in the same VNET as that of AKS cluster ?
Or you can have a VM in different VNET but that VNET needs to be paired with VNET of AKS cluster.
See different ways of connecting to private AKS cluster:
To quickly test it out you can use the command-invoke (Example below)
https://learn.microsoft.com/en-us/azure/aks/command-invoke
az aks command invoke \
--resource-group myResourceGroup \
--name myPrivateCluster \
--command "kubectl get pods -n kube-system"
Let us know if that helps !
Regards,
Shiva.