When copying workflows using the ShareGate migration tool, the workflow status, history and tasks will not be preserved.
For example, when migrating a list with an approval workflow, the following information will not be preserved on the list items:
Unfortunately, there are no SharePoint APIs (Client or Server) that allow the preservation of the content of the workflow task and workflow history lists. The status is linked to the tasks and since these cannot be migrated, the status can't be preserved. In theory, the ShareGate migration tool could preserve this information by directly modifying the underlying database of the server, but doing so would void the warranty on the SharePoint installation. Hence, the ShareGate migration tool does not support the migration of workflow tasks and workflow history.