Good day @Patrick ,
It's great question and you are probably right. I made a short search and I did not found any documentation on doing so. With that being said, this is really simple and there are multiple option to make a copy of the database but if you want to take the safe road then your best solution is probably to create Transactional replication and to push the data to the Azure SQL Database. For more information about Transactional replication with Azure SQL Managed Instance, check the following document:
Note 1: Azure SQL Data Sync does not support Azure SQL Managed Instance.
Note 2: Using Export and import is not a safe way since using bacpak does NOT guarantee transactional consistency ! You might lose data or worse get data which is not consistent