If you seek good coverage, you undoubtedly would be better off moving that against the public interface.

"private" tests are more for like when you're having trouble figuring out an edge case failure and want to narrow it down to a specific helper function to aid debugging or if you need help coming up with the right design for an internal function. As before, we're talking exceptional circumstances. Rarely would you need such a thing. But if it helps, no need to fear it.

Either way, I'm not sure you would be looking for good coverage, only the bare necessities to reach the goal. Once settled, the tests are disposable. Organizing your project into internal libraries in case you encounter a debugging problem in need of assistance, for example, is extreme overkill.