Hey,
Can you please confirm what is the .bak file created from?
is it a SQL server?
Because you cannot restore .bak file in Azure Synapse as Azure Synapse is an MPP (OLAP) unlike other MSFT databases.
What is the use case/downstreams of the new database?
Depending on that we can split our thoughts between Azure SQL DB or SQL MI.
SQL MI is a costly affair unlike Azure SQL DB but is a case of lift and shift scenario.
https://www.mssqltips.com/sqlservertip/7718/azure-sql-managed-instance-vs-azure-sql-database/