It's neither about TDD or BDD.

It’s neither about TDD or BDD. And we are not talking about specific paradigm (e.g., OOP vs functional). I guess we agree we need to assert contracts and not implementation details.

By contract I mean the set of public APIs of your code.

It’s not about classes. If you have a C file with 2 functions exposed by its header and all other functions being “private” to the translation unit, you need to test only these 2 “publicly exposed” functions.

If any line of code is not reachable from the public APIs, chances are you didn’t apply TDD well (or at all).