How to create a master key on the master database?What are the roles required to GRANT to the login and user of the master db for the same?
I don't believe it's possible, or useful to CREATE MASTER KEY in the master database in Azure SQL Database/Azure Synapse Analytics (formerly SQL Data Warehouse).  And the error you're seeing is a bit misleading, as you get that error whenever you attempt an operation in master that is allowed in normal SQL Server, but prohibited in Azure SQL Database.

The Database Master Key (DMK) in the master database is used to protect Certificates and Asymmetric Keys in master, but you can't create either of those in the master database in Azure SQL Database.  And in normal SQL Server the DMK in master protects the Database Encryption Keys (DEK) for Transparent Database Encryption (TDE) of user databases.

The encryption hierarchy for TDE in Azure SQL Database works differently:


  Transparent data encryption encrypts the storage of an entire database
  by using a symmetric key called the database encryption key. This
  database encryption key is protected by the transparent data
  encryption protector. The protector is either a service-managed
  certificate (service-managed transparent data encryption) or an
  asymmetric key stored in Azure Key Vault (Bring Your Own Key). You set
  the transparent data encryption protector at the server level for
  Azure SQL Database and Data Warehouse, and instance level for Azure
  SQL Managed Instance.