Hi Jose Augusto Baltazar - Thanks for reaching out over Q&A Forum.
Based on the details provided, yes if the access level of the container is set to private, you need to pass some valid auth in order to access the blob else it would result into error.
Now, there is access level which is also controlled on the account level as well apart from the container one which will tend to overwrite what's there on the container level. Kindly review that once.
https://zcusa.951200.xyz/en-us/azure/storage/blobs/anonymous-read-access-configure?tabs=portal
Further you mentioned that you are leveraging MI however in that case, it should ideally with RBAC permissions provided you have Reader on the Management Plane and Storage Blob Data Reader on the Data plane provided. To verify what's the auth getting passed, I would suggest enabling logging which shall tend to point the same such as SAS, Access Key, OAUTH (AD)
https://zcusa.951200.xyz/en-us/azure/storage/blobs/monitor-blob-storage?tabs=azure-portal
Lastly, I am assuming currently there are no networking level restriction on the account level.
Hope that helps!
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