If the test is in the API testset, it's API. If it isn't, it's an implementation detail.
> What if tests had undisputable bug?
If it's in the API testset, time for a major version bump. If not, fix it.
> Test refactoring requires major release now?
Only if you're refactoring the API, as defined by the API testset, thereby producing a breaking change.
> Realistically test suite will have some execution paths not covered.
Doesn't matter. If the behavior isn't in the API testset, it's not a part of the API.
> But I disagree that it would automate semver.
The point isn't to automate semver, I'm not even sure what that would mean. It's to define it, in a useful and objective way.