You need to drain the node pool, as already answered :
kubectl get nodes (this will give you the correct name, which is longer than the short version from azure portal)
example: aks-nodepool1-00000000-vmss000000
then:
kubectl drain node-name --delete-local-data --ignore-daemonsets
and after that, you need to assign the new pool as a system pool:
az aks nodepool update -g myResourceGroup --cluster-name myAKSCluster -n mynodepool --mode system
where mynodepool is the short name.
AKS requires you to assign your new pool as the system pool manually, before deleting the old one, otherwise you wold be without system pools.
Reference:
https://learn.microsoft.com/en-us/azure/aks/use-system-pools