Please document the new function in docs/changelog.rst and docs/api.rst.

I agree to not add Python 3.12 support.

It's tempting to add Python 3.12 support, but Python 3.12 semantics is different:

static inline void _Py_SetImmortal(PyObject *op)
{
    if (op) {
        op->ob_refcnt = _Py_IMMORTAL_REFCNT;
    }
}

• Different API: it has no return value (void)!
• It doesn't reject Unicode objects.
• It doesn't untrack objects in the GC.

// Immortal objects were implemented in Python 3.12, however there is no easy API
// to make objects immortal until 3.14 which has _Py_SetImmortal(). Since
// immortal objects are primarily needed for free-threading, this API is implemented
// for 3.14 using _Py_SetImmortal() and uses private macros on 3.13.

I agree that PyUnstable_SetImmortal() is mostly useful on free-threaded builds, so it's ok to skip Python 3.12.

LGTM.