I've added a Requirement-based test suites in Test Plans with one test case inside. Obviously, the test case is linked to a Work Item in Backlog.
The problem is I when I go to backlog board section (/_backlogs/board/Backlog%20items), I cannot see the tests on the related work item: 
Now, if I quickly add a test on work item via Backlog Items (and not Test Plans): 
all the previous tests suddenly shows up:
So, is there anyway to make Test section of work items always visible?
You've got expected behavior, only when test cases are created from the Kanban board and updated afterwards in Test Manager, the Kanban board shows the correct status. Check the section Test status in the Kanban board at website below:
https://learn.microsoft.com/en-us/vsts/work/kanban/add-run-update-tests?view=vsts
Test integration with the Kanban board makes it easy for teams to get started with manual testing and then take advantage of the full testing capabilities in Test Manager later, when required. When test cases are created from the Kanban board and updated afterwards in Test Manager, the Kanban board shows the correct status. However, integration is not optimized to work in the other direction; for example, when users create requirement-based suites with Test Manager instead of in the Kanban board. We intend to make some major performance improvements to this integration in future releases.
