@Otilia Zverchea These features are supported by Azure Blob Storage.
Azure Blob storage - Last access time tracking now generally available
You can also use the last access time of objects to define lifecycle management rules for moving blobs to cooler access tiers when they haven't been accessed for a specified duration. In addition, enabling auto-tiering with your lifecycle rule will automatically move the object back into a hotter access tier upon access. This update extends the access time tracking and associated lifecycle management support added earlier for Azure Blob storage to Data Lake Storage.
For Azure Files, I do not believe those features are available yet.
Please refer to this post for alternatives:
https://stackoverflow.com/questions/61419028/last-access-time-of-the-azure-storage-files