I think it's far more accurate to say that Cython is a programming language of its own that is a hybrid of Python and C++, that happens to produce CPython extension modules when compiled.
The performance benefits are really achieved by incrementally changing your Python code to something that looks a lot more like C(++).
This is also reflected in the Cython documentation which literally mentions the "Cython language".
Cython is great as an alternative to writing C extension modules for performance reasons or to creating bindings to libraries written in C or C++. It's not so great just to make Python applications faster as it's not fully compatible[1].
[1]: https://cython.readthedocs.io/en/latest/src/userguide/limita...