From the error code you have provided (10060) I'd guess that's a firewalling issue:
An error has occurred while establishing a connection to the server.
When connecting to SQL Server, this failure may be caused by the fact
that under the default settings SQL Server does not allow remote
connections. (provider: TCP Provider, error: 0 - A connection attempt
failed because the connected party did not properly respond after a
period of time, or established connection failed because connected
host has failed to respond.) (Microsoft SQL Server, Error: 10060)
I have found this within the Azure Data Factory documentation
To access the SQL Managed Instance public endpoint, you can use an
Azure Data Factory managed Azure integration runtime. Make sure that
you enable the public endpoint and also allow public endpoint traffic
on the network security group so that Azure Data Factory can connect
to your database.
So it seems you need to open and properly configure your SQL MI's public endpoint. More information on this can be found here: Configure public endpoint in Azure SQL Managed Instance.
If your are willing/able to migrate your database from SQL MI to a SQL DB you can also make use of a managed private endpoint. It would establishe a private link to your database and keep your data on Microsoft's backbone. Unfortunately Azure SQL Managed Instances
are currently not supported.