When you start a PITRrestore in your Managed Instance, is very useful be able to track how it progresses. Azure Portal does not show too many details about it, but we can use Managed Instance logs to track it.
The way to do it, is quite simple. You just need to connect to your MI using your SSMS (SQL Server Management Studio) and open "SQL Server Logs" that you will find under "Management"
After openlogs, is the time to filter then to be focus on the recovery process.
After applying the filter, you will be able to track restore progression.