Looking for a method to export data outside of the Azure Cost Centre into a storage account. This can't be done because of network restrictions on a storage account (i.e. firewall rules with selected networks prevents the Azure Cost Centre from exporting data to a storage account).
what is the workaround? Can a datafactory do this instead with APIs? Can an Azure function do this? what are some of the options available?
No, Both Logic App and Azure Data Factory has no connector to Azure Cost Centre.
Yes, you can use function to do this. You can do a Http request to get data from Azure Cost Centre and then upload a file with that data to Storage Blob.