Hello Artem Shaturskyi,
Thank you for posting your question in the Microsoft Q&A forum.
Using Microsoft Entra ID authentication for direct blob access. Instead, it is designed for internet-facing scenarios and is optimized for publicly accessible blobs. To authenticate blob access you may try SAS (Shared Access Signature) with FrontDoor. Refer Microsoft doc link - https://learn.microsoft.com/en-us/azure/frontdoor/scenario-storage-blobs
For direct blob access with Microsoft Entra ID authentication, you can use Azure Storage, which supports Microsoft Entra ID to authorize requests to blob data. Refer Microsoft doc link - https://learn.microsoft.com/en-us/azure/storage/blobs/authorize-access-azure-active-directory
Please let me know if this helped to resolve the issue on your side. Please remember "Accept Answer" if above reply helped, so that others in the community facing similar issues can easily find the solution.