So you can copy Azure SQL Database using the Azure Portal, PowerShell, Azure CLI, and T-SQL. However, this functionality is limited to Azure SQL Database and does not work for Azure Synapse databases (a.k.a. SQL Pools). Early in 2021, the ability to use the copy functionality to copy databases between subscriptions is also supported but requires security work to make sure the permissions in the database servers and networking allow that to happen.
There’s a lot involved in the process, leaving me to provide the sage wisdom that it’s easier not to put it in the wrong subscription to begin with if you can avoid it.