No, .bacpac Import/Export does not support authentication types beyond those exposed in the Powershell you linked. You can use SQL auth or ADPassword auths, for the object which is assigned as the AD admin of your SQL Server. If you are only removing SQL auth, you could investigate whether the ADPassword option meets your needs.
Managed Service Identity does not really make sense for Import/Export. Which identity do you want to use?
MSIs are used to allow some Azure resources to authenticate to another Azure resource. For instance, if you create a VM, on which you deploy your code, which then authenticates to (for example) your Azure Storage, to do whatever the permissions that identity is assigned.
In contrast, Import/Export is not a resource to which an identity could be assigned, it is an operation you can take on your server. Behind the scenes, we need to authenticate to your server, but since this is running in our infrastructure there is no logical identity it could use.
I hope this information is helpful
Regards
Geetha