Hi,
Yes, Standard S2 SKU supports VNet integration. Below article has more information on vnet integration:
https://learn.microsoft.com/en-us/azure/app-service/overview-vnet-integration
Below article has more information on securing your storage account using private endpoint. Your function app could connect to your storage account via private endpoint without enabling public access.
Use private endpoints for Azure Storage
https://learn.microsoft.com/en-us/azure/storage/common/storage-private-endpoints
Please click Accept Answer if the above was useful.
Thanks.
-TP