(Included as an answer due to character limitation)
The following are all the access and identity options for AKS documentation:
https://learn.microsoft.com/en-us/azure/aks/concepts-identity
Identity creating and operating the cluster permissions
Microsoft.Compute/diskEncryptionSets/read
Microsoft.Compute/proximityPlacementGroups/write
Microsoft.Network/applicationGateways/read
Microsoft.Network/applicationGateways/write
Microsoft.Network/virtualNetworks/subnets/join/action
Microsoft.Network/publicIPAddresses/join/action
Microsoft.Network/publicIPPrefixes/join/action
Microsoft.OperationalInsights/workspaces/sharedkeys/read
Microsoft.OperationalInsights/workspaces/read
Microsoft.OperationsManagement/solutions/write
Microsoft.OperationsManagement/solutions/read
Microsoft.ManagedIdentity/userAssignedIdentities/assign/action
AKS cluster identity permissions
Microsoft.ContainerService/managedClusters/*
Microsoft.Network/loadBalancers/delete
Microsoft.Network/loadBalancers/read
Microsoft.Network/loadBalancers/write
Microsoft.Network/publicIPAddresses/delete
Microsoft.Network/publicIPAddresses/read
Microsoft.Network/publicIPAddresses/write
Microsoft.Network/publicIPAddresses/join/action
Microsoft.Network/networkSecurityGroups/read
Microsoft.Network/networkSecurityGroups/write
Microsoft.Compute/disks/delete
Microsoft.Compute/disks/read
Microsoft.Compute/disks/write
Microsoft.Compute/locations/DiskOperations/read
Microsoft.Storage/storageAccounts/delete
Microsoft.Storage/storageAccounts/listKeys/action
Microsoft.Storage/storageAccounts/read
Microsoft.Storage/storageAccounts/write
Microsoft.Storage/operations/read
Microsoft.Network/routeTables/read
Microsoft.Network/routeTables/routes/delete
Microsoft.Network/routeTables/routes/read
Microsoft.Network/routeTables/routes/write
Microsoft.Network/routeTables/write
Microsoft.Compute/virtualMachines/read
Microsoft.Compute/virtualMachines/write
Microsoft.Compute/virtualMachineScaleSets/read
Microsoft.Compute/virtualMachineScaleSets/virtualMachines/read
Microsoft.Compute/virtualMachineScaleSets/virtualmachines/instanceView/read
Microsoft.Network/networkInterfaces/write
Microsoft.Compute/virtualMachineScaleSets/write
Microsoft.Compute/virtualMachineScaleSets/virtualmachines/write
Microsoft.Network/networkInterfaces/read
Microsoft.Compute/virtualMachineScaleSets/virtualMachines/networkInterfaces/read
Microsoft.Compute/virtualMachineScaleSets/virtualMachines/networkInterfaces/ipconfigurations/publicipaddresses/read
Microsoft.Network/virtualNetworks/read
Microsoft.Network/virtualNetworks/subnets/read
Microsoft.Compute/snapshots/delete
Microsoft.Compute/snapshots/read
Microsoft.Compute/snapshots/write
Microsoft.Compute/locations/vmSizes/read
Microsoft.Compute/locations/operations/read
Additional cluster identity permissions - Needs to be added to the cluster identity after it's created.
Microsoft.Network/networkSecurityGroups/write
Microsoft.Network/networkSecurityGroups/read
Microsoft.Network/virtualNetworks/subnets/read
Microsoft.Network/virtualNetworks/subnets/join/action
Microsoft.Network/routeTables/routes/read
Microsoft.Network/routeTables/routes/write
Microsoft.Network/virtualNetworks/subnets/read
Microsoft.Network/privatednszones/*
As a single list, that would be:
Microsoft.Compute/diskEncryptionSets/read
Microsoft.Compute/disks/delete
Microsoft.Compute/disks/read
Microsoft.Compute/disks/write
Microsoft.Compute/locations/DiskOperations/read
Microsoft.Compute/locations/operations/read
Microsoft.Compute/locations/vmSizes/read
Microsoft.Compute/proximityPlacementGroups/write
Microsoft.Compute/snapshots/delete
Microsoft.Compute/snapshots/read
Microsoft.Compute/snapshots/write
Microsoft.Compute/virtualMachines/read
Microsoft.Compute/virtualMachines/write
Microsoft.Compute/virtualMachineScaleSets/read
Microsoft.Compute/virtualMachineScaleSets/virtualmachines/instanceView/read
Microsoft.Compute/virtualMachineScaleSets/virtualMachines/networkInterfaces/ipconfigurations/publicipaddresses/read
Microsoft.Compute/virtualMachineScaleSets/virtualMachines/networkInterfaces/read
Microsoft.Compute/virtualMachineScaleSets/virtualMachines/read
Microsoft.Compute/virtualMachineScaleSets/virtualmachines/write
Microsoft.Compute/virtualMachineScaleSets/write
Microsoft.ContainerService/managedClusters/*
Microsoft.ManagedIdentity/userAssignedIdentities/assign/action
Microsoft.Network/applicationGateways/read
Microsoft.Network/applicationGateways/write
Microsoft.Network/loadBalancers/delete
Microsoft.Network/loadBalancers/read
Microsoft.Network/loadBalancers/write
Microsoft.Network/networkInterfaces/read
Microsoft.Network/networkInterfaces/write
Microsoft.Network/networkSecurityGroups/read
Microsoft.Network/networkSecurityGroups/write
Microsoft.Network/privatednszones/*
Microsoft.Network/publicIPAddresses/delete
Microsoft.Network/publicIPAddresses/join/action
Microsoft.Network/publicIPAddresses/read
Microsoft.Network/publicIPAddresses/write
Microsoft.Network/publicIPPrefixes/join/action
Microsoft.Network/routeTables/read
Microsoft.Network/routeTables/routes/delete
Microsoft.Network/routeTables/routes/read
Microsoft.Network/routeTables/routes/write
Microsoft.Network/routeTables/write
Microsoft.Network/virtualNetworks/read
Microsoft.Network/virtualNetworks/subnets/join/action
Microsoft.Network/virtualNetworks/subnets/read
Microsoft.OperationalInsights/workspaces/read
Microsoft.OperationalInsights/workspaces/sharedkeys/read
Microsoft.OperationsManagement/solutions/read
Microsoft.OperationsManagement/solutions/write
Microsoft.Storage/operations/read
Microsoft.Storage/storageAccounts/delete
Microsoft.Storage/storageAccounts/listKeys/action
Microsoft.Storage/storageAccounts/read
Microsoft.Storage/storageAccounts/write