Third normal form or not has no relation the choice between Azure SQL Database and Azure MI.
I think Azure SQL Database would be your first choice, not the least from a price perspective. But you would go with Azure MI if you need things not supported in SQL Database. (CLR, Service Broker, Cross-DB queries, Agent to mention a few things.) Also, if you are doing a lift-and-shift from a on-prem solution, MI can be less pain than going to Azure SQL DB.
But 3NF or not has nothing to do with it.