In Mahayana Buddhism is it the true self that is reborn, or the empirical self?
I tend to see it described as if it's just the latter that is, but then if I am my true self then doesn't that equate to annihilationism and nihilism?
There is no rebirth or reincarnation in the sense that the soul takes on a new body (rebirth / reincarnation) after death. (In Sinhala Punarupathi)
In Buddhism conception which is the continuation of the Bhava from end of the previous life (death) in the cycle of Samsara. (Punarbhava)
In other words this is a process in which there are events like birth and death. In the light that there is no everlasting unchanging core this is not a rebirth as it is not the person from the previous existence nor it is a entirely different being, but just the continuous flow of the process of becoming.
Continuation of a core entity (rebirth / reincarnation) is a Hindu concept. Buddhist concept is the continuation of the process.
Since there is a continuation (of the process), all doesn't end with death.
The confusion about rebirth is due to rebirth being used in Buddhist translation due to the limitations of the vocabulary and there is no better world to use.
(I am not sure if this fits into the Maha Yana take on the matter. )
True self is a phrase that comes up in Chan/Zen. It sometimes considered indistinguishable from the idea of an eternal soul, but never stated so clearly as that.
Empirical self, according to google is a phrase used by Kant, the psychologist William James, and I suppose it has a man in the street definition of "who you are in the sense of what is empirically provable, observable." I don't claim to understand Kant, and I don't have time to read James, I'll use the man in the street definition.
The Mahayana philosopher who put the most thought into the question of eternalism vs extinctionalism is Nagarjuna, who came up with a two truth's doctrine, that there is a truth for the ordinary world and a truth for the transcendent, supermundane, supernatural world. I don't actually follow Nagarjuna's arguments, it's somewhat abstruse. I think he means to say in the conventional sense of truth, we're dead, in the transcendent truth, there wasn't a difference between being alive and dead.
He also rejected that we were eternal, and rejected that we would become extinct (die for good), and appealed to a middle between these as the appropriate belief. This defies my man in the street sense of logic (mortality and immortality seem pretty exclusive and opposite), but I've read that this can also be interpreted to mean that they are both possibly true, meaning it's a statement with multiple truth values, (true, false, and just don't know) and this statement about life after death isn't true, isn't false, so that leaves "just don't know".
And that gets us to having to deal with life after death on faith, which is certainly a Mahayana concept.