A frequently-presented objection to the concept of writing automated tests is that it ossifies the implementation of the system under test. “If I’ve got all the tests you’re proposing,” I hear, “then I won’t be able to make any changes without breaking the tests.” There are two aspects to this problem.
Tests should make assertions about the externally-observable behaviour of the system under test. If you have tests that assert that a particular private method does its thing in a particular way, then yes, you are baking in the assumption that this private method works in a particular way. And yes, that makes it harder to change things. But it isn’t necessary.
Any test that is no longer useful is no longer useful: delete it. Those tests that helped you to build the thing were useful while you were building the thing: if they’re not helping you now then just get rid of them.
When you’re building a component, you’re probably thinking quite deeply about the algorithm it will implement, and how it will communicate with its collaborators. Thinking about those will mean writing tests about them, and whenever those tests are in the suite they’ll require the algorithm be implemented in a particular way, and that the module talk to its collaborators in a particular way. Do you no longer care about those details, as long as it does the right thing? Delete the tests, and just keep the ones that make sure it does the right thing.