在对已删除的工作项进行更新时，需要使用“编辑”操作而非“更新”操作。具体代码示例如下：

WorkItemTrackingHttpClient witClient = connection.GetClient();

JsonPatchDocument patchDocument = new JsonPatchDocument();
patchDocument.Add(new JsonPatchOperation()
{
    Operation = Operation.Replace,
    Path = "/fields/System.State",
    Value = "Active"
});

WorkItem updatedWorkItem = await witClient.UpdateWorkItemAsync(patchDocument, workItemId, null, true);

需要将上述代码中的 Operation = Operation.Replace 改成 Operation = Operation.Test，然后添加如下代码：

// Test the current state of the work item
WorkItem workItem = await witClient.GetWorkItemAsync(workItemId);
if (workItem.Fields["System.State"].ToString() != "Removed")
{
    // If the work item is not in the "Removed" state, use the "Update" operation to modify it
    updatedWorkItem = await witClient.UpdateWorkItemAsync(patchDocument, workItemId, null, true);
}
else
{
    // If the work item is in the "Removed" state, edit it instead of updating it
    updatedWorkItem = await witClient.EditWorkItemAsync(patchDocument, workItemId);
}

这段代码会先通过 GetWorkItemAsync 方法获取工作项的当前状态，然后判断状态是否为“删除”（"Removed"），若状态为“删除”，则使用 EditWorkItemAsync 方法进行修改，否则使用 UpdateWorkItemAsync 方法进行修改。这样就可以规避 “Field state 'Active' not supported when Work Item has been "Removed"” 这个错误了。