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Do all Buddhists say that nirvana exists? I can't believe I don't know the answer to that question, the amount I've read about Buddhism.
Off the top of my head, some say it has svabhava, those that equate it with emptiness probably say it does not have svabhava, and some say it is the self.
Nibbana is an element (dhatu).
There are these two elements:
Dve imā, ānanda, dhātuyo—
the conditioned element and the unconditioned element.
saṅkhatādhātu, asaṅkhatādhātu.
When a mendicant knows and sees these two elements,
Imā kho, ānanda, dve dhātuyo yato jānāti passati—
they’re qualified to be called ‘skilled in the elements’.
ettāvatāpi kho, ānanda, ‘dhātukusalo bhikkhū’ti alaṃvacanāyā”ti.
MN 115
The Pali suttas use the term "sa dhatu" rather than "sabhava".
Mendicants, whether Realized Ones arise or not, this element persists, this regularity of natural principles, this invariance of natural principles:
Uppādā vā, bhikkhave, tathāgatānaṃ anuppādā vā tathāgatānaṃ, ṭhitāva sā dhātu dhammaṭṭhitatā dhammaniyāmatā.
AN 3.136
The term "sabhava" has a valid meaning in Theravada Commentary but because the term contains the word "bhava" (which has different meanings & can mean "ego"), the Mahayana misconstrue "sabhava" and use for for their propaganda. Also, the Mahayana teaches emptiness different to the Buddha. Mahayana exists because people have different ideas. In the Pali suttas, the term "emptiness" does not mean "empty of inherent existence". It means empty of "ego" or "I-thinking" & "my-thinking". Theravada does not concern itself with whether "things" exist or not. Theravada only concerns itself with ending suffering; which occurs with the ending of craving, attachment & egoism. If I believe a computer exists, this does not cause suffering. Suffering only occurs when I regard a computer as "my computer".
I think all Buddhists say there is Nirvana.
It's true that in Mahayana Buddhism, Nirvana does not have svabhava. In this question, I tried to link Theravada emptiness to Mahayana emptiness. My understanding of this is that Nirvana does not have the inherent essence given to it by mental reification. This means Nirvana is not what you imagine it to be, but it does not mean that it does not exist. It means that the mental idea that I have of Nirvana is non-existent.
However, a disagreement between Theravada and Mahayana is on the topic of whether Nirvana and Samsara are the same, or completely different. This answer may have the right explanation to the fact that probably there is no disagreement after all. I quote it here:
Samsara is Nirvana in at least two senses:
Nirvana is achieved here, in this world (="samsara"). We don't fly to another planet or go to other dimension when we achieve Nirvana; our perception changes, and so does our subjective reality.
Samsara is Nirvana because we should stop trying to escape. Trying to escape "this" is what makes it Samsara. The idea of otherworldly Nirvana is exactly the kind of craving that leads to suffering. Samsara is Nirvana means one has stopped craving. That is called cessation.
So, ultimately, there may be no real disagreements between Buddhist traditions on Nirvana.
