Not able to Create Database or Restore Database on the Azure SQL Managed Instance

Crikey, this is one of those "no idea how I fixed it" things.

Before I went to lunch, I could reliably generate the error in question by running the provided T-SQL, yet when I came back from lunch the BACKUP command completed fine!

The main thing I remember changing was on the Azure side, where I created a SAS (Shared Access Signature).

This is supposedly not required for SQL 2014 as it uses an actual Azure Credential to connect to the storage instead. I actually created the SAS for an instance of SQL Server 2016 that I want backing up to the same container, and that may have opened the access pathway to the container for SQL Server 2014 too!

Many thanks to Sean Gallardy for recommending ProcMon, which showed a whole ton more error log information than the "ErrorCode=(5)Access is denied" message did.

Most likely, you have multiple Differential backups in your DB_NAME_DIFF.bak file, and the restore is picking one that occurred before the most recent FULL. As I hinted in my comment, and Scott stated in his.

Edit the following to check for multiple files in a backup device:

RESTORE HEADERONLY   
FROM DISK = N'C:\AdventureWorks-FullBackup.bak'   
WITH NOUNLOAD;  
GO