It's common that if you extract a function or a module with a well defined interface, that function or module can't tell whether a "bad" input indicates an expected or an unexpected error.

For example division by zero often indicates an "unexpected" error, but it wouldn't if you were implementing a spreadsheet.

So to me the approach of using different forms of error reporting for the two kinds of error doesn't seem promising: if you imagine you had to implement division yourself, which kind of error should it report? Should you have two variants of every fallible function so the caller can choose?