On this page you find how you can create a Synapse Linked Service:
azurerm_synapse_linked_service | Resources | hashicorp/azurerm | Terraform Registry
The attribute type_properties_json requires a json object with the properties for a specific linked service.
It is very difficult to find the proper properties for a certain linked services. Maybe you can point to this link as a reference:
Linked Service - Create Or Update Linked Service - REST API (Azure Synapse) | Microsoft Docs
You find the needed properties per resource type