@AzureKnwGt-8579 Thanks for posting this question in Microsoft Q&A. If you are deploying your functions in consumption plan it will support run functions from a package using the storage URL but it doesn't support virtual networking and other options.
Regarding your second question automating the artifact from Jfrog to Blob storage via private network.
As the per JForg documentation I dont see any option to access the storage account artifacts via selected networks or through disabling public networks since this is an integration with 3rd party, I suggest you check with JForg support team .
Alternatively, as a workaround I see that JForg have these rest API that might be helpful for your requirement. You can create a logic app using the http action to download the content of artifact and thereby using the create blob action to create blob in your storage account.
Hope this helps, let me know if you have any questions on this.