Connecting Data Factory To Synapse Using A Private Endpoint

I am trying to setup a Linked Service in Data Factory to Synapse using a private endpoint IP address. When using the Data Factory wizard to set up a Linked Service to a Synapse, it generates this connection string:

Integrated Security=False;Encrypt=True;Connection Timeout=30;Data Source=workspace.sql.azuresynapse.net;Initial Catalog=database;

This works fine. However, I am required to use the private endpoint IP addresses instead of the public hostname. The private endpoint has already been created. When replacing the hostname with the private IP address, it results in this error:

Cannot connect to SQL Database. Please contact SQL server team for further support. Server: '10.10.10.10', Database: 'database', User: ''. Check the linked service configuration is correct, and make sure the SQL Database firewall allows the integration runtime to access. A connection was successfully established with the server, but then an error occurred during the login process. The target principal name is incorrect.

Following some advice on online, I have changed the connection string to remove the Encrypt=True; and added TrustServerCertificate=True. However, this results in another error:

Cannot connect to SQL Database. Please contact SQL server team for further support. Server: '10.10.10.10', Database: 'database', User: ''. Check the linked service configuration is correct, and make sure the SQL Database firewall allows the integration runtime to access. Cannot open server "10.10.10.10" requested by the login. The login failed.

A user has been created in the Synapse database for the Data Factory System Managed Identity, and this works when using the public hostname, why does it not work when using the private endpoint IP address?