Hi,
Here is a quote from one of the MI team:
The upgrade from the standard-series SQL MI to one of the premium-series offers (and back, if needed) is easy to do. It’s a executed as a standard Azure SQL instance scaling operation (similar to changing the number of vCores or reserved storage size for the instance) -> it’s a fully managed, online, async workflow (customer can continue to use their instances while the operation is being performed).
And for full answer you can check this doc:
So the short answer is that it is possible and you can continue working on the database while doing so. Check the document for more info before you start