@Taka Thanks for reaching out to Microsoft Q&A. I understand that you are unable to access the Azure File Service via the SAS URL you found under the Storage Level whereas you were able to access the individual file.
Can you please share more details regarding your use case and why you want to access Azure File Service using REST API? Usually, you would add the File Share as a mount to access the files in the share using SMB or NFS. Is there any reason you are using Azure File Service via REST APIs?
Please check out the different storage options available in Azure and when to use the same- https://learn.microsoft.com/en-us/azure/storage/common/storage-introduction?toc=%2Fazure%2Fstorage%2Fblobs%2Ftoc.json#sample-scenarios-for-azure-storage-services
Looking forward to hear from you. Thank you!