The following is taken from my longer article on this subject. This quote is jumping in at the end of that article, but it summarizes my answer to the question asked. This answer may not seem to respond to the OP’s question as asked because it is coming from the non-conventional view, but it is responding to the incorrect view encoded in the question. The OP is very clear about what he/she/they is asking, but from the non-conventional view the question is meaningless. The Two-Truths doctrine is important to our understanding, but it shouldn’t be a justification for making-believe we still understand the conventional world today as humanity once did two and a half millennia ago.
"Forms are Empty, Emptiness is Form"
...please note that Emptiness is not Suchness, and is not the nature of anything—because then suchness wouldn’t be empty of an intrinsic self. We can say it is the essence of Suchness, elevating the absence of what we thought was there in the appearances to the stature of the absolute source of all, but that is just overkill and so wrong. It’s useful for a while, but it has the nasty effect of retarding our progress.
“Know that pointing out appearances as mind and mind’s nature as emptiness (thus making the duality of appearances and emptiness into a unity) is not the method of Nyingtik pith instruction. Such instruction may be given occasionally, but only as a provisional means to elevate the mind of an individual initiate, certainly not as a definitive truth.”
“Neither existence nor nonexistence nor space-time is to be found here. Appearances and emptiness are indistinguishable, so that neither eternity nor the void are anywhere perceptible.”
(Quotes above attributed to Longchenpa in the “Yeshe Lama,” Jingme Lingpa)
Suchness is the presencing of forms (otherwise there would be no distinguishing anything), and forms are empty of any intrinsic self. Yet we can discern the inherent essence of each form. Where we get lost is in confusing the “nature” (inherent essence) of a form, which sets it apart from other forms, with an intrinsic self. Our problem lies in the confusing multiplicity of meanings for the word “nature.” If we just thought of it as “intrinsic self-naturing” versus “essential character,” we'd be on our way to lessening our confusion.
Thus, “Emptiness” (note the capitalization) is a form also—it’s a thought form, called a “concept.”
So repeat after me: “Forms (suchness) are empty, Emptiness is form.” This will remind us that “Emptiness” is just an idea that took hold when we noticed we were originally wrong about everything.
The essential character of Suchness is Pure Spontaneous Presencing. And I feel the need to again remind you that suchness is not a thing, it's the name we give to this activity—“presenting as form.”
And the nature of this is not something else, it’s the activity. So Pure Spontaneous Presencing is not a thing. It’s simply a description of the salient characteristics of the activity that is our phenomenal existence—of suchness.
Thus, it defines nothing, because there is nothing to define. As Garab Dorje said:
“Transcending all discrimination in its arising, Transcending all discrimination in its release.”
And as Jigme Lingpa said:
“While safeguarding the continuity of the wonderful intrinsic perfection of our existential presence, if the thought “the nature of pure presence is empty” springs up in the rational mind, by ascribing an objective focus of emptiness to pure presence, buddha is precluded.”
Forms are empty, Emptiness is form.
Addendum in response to the OP’s comment to this answer (placed here because of length)
By “permanent” you mean all of time? Time is the epitomization of arising and passing away—tick toc, tick toc—so would we say Time “itself” is permanent? I think we do, and yet even scientists are starting to say Time is just a convention that organizes events into orderly sequences. They are being forced into accepting a Two Truths doctrine because they and we share the same reality (i.e., Buddhism is right on this point). We say Time arises and passes away, but our experience of the arising and passing away of all things is only contingently factual because Time as we conventionally understand it, doesn’t exist.
But what does that word “reality” mean? The set of all events? A container in which everything “comes to pass”? What’s missing here?
It’s the motivating ‘force’, which in Buddhism is sometimes called “emptiness”. (It’s a terrible word because it’s an abstracted quality of all that manifests, but we conventionally use it as if it is something, but it’s truly only the absence of any intrinsic self-nature.)
So how did the absence of something become a motivating force? Habit. Lazy thinking. Misunderstanding. Because the truth is more bizarre than we imagine. Pick one.
The word “Emptiness” is a dialectical term. This means that when you apply it to things, you are asserting that they have no substance, no self, no intrinsic self-nature. And when you apply it to Emptiness, that also is without substance, no self, and no intrinsic self nature. It all just dissolves away. Thus, as you mentioned, Nagajuna said Emptiness is empty, which means Emptiness is just a mental form that has no intrinsic existence, but also that there is no Nature—just naturing.
So no, Emptiness is not permanent, because even what it points to (the absence of an intrinsic self-nature) is ultimately empty of meaning.
And because Time is not permanent, nothing that exists is permanent.
But your comment opens up the possibility of looking for something “relatively” permanent. Is there some conventional quality of experience that does not arise and pass away?
Emptiness is empty, awareness stops and starts in lockstep with what arises, so what’s left?
The motivating ‘force’, which is called Mahākarunā in Buddhism (or just Buddha nature, but that sounds like some thing). This simply means that stuff shows up in response to extant conditions. But not deterministically because the responses are stochastic in character and show a certain drift or creativity in what actually happens. The show is endless and it is spontaneous—but always coherent in some way from appearance to appearance. This is conventionally so, but not because we are ordering the appearances, but because the truth is a little bit different.
What is Reality? The Absolute truth? Time is impermanent, and not to be found absolutely. Awareness therefore is empty of meaning, for what would an awareness of no duration be? Emptiness is empty, as we said. So how, and to what, does Buddha nature respond?
This. This is all there is. The past is just the conventionally ordered conditions that made This possible, and they are intrinsic to This, not something attached like a string of moments of time that we remember. The Now we conventionally speak of as being the time that This is happening is not a moment in time because there is no such thing. Rather, it’s a vignette consisting of the conditions and the response to the conditions—all showing up Now—without any intrinsic substance or self. Just This, awesome beautiful display. And it never ends because it never begins. All there is, is this Now. That’s the stage. The how is beyond thought.
So to recap, conventionally, the appearances show up, and that is true. Ultimately, there is only the responsive naturing of appearances, and because time doesn’t exist ‘we’ somehow manage to organize these appearances into a moving image—the prior images in the sequence being the conditions intrinsic within the vignette Now. It’s like the entire ‘universe’ is just the imputed motion in a sequence of still images in an endless epiphanic display of Mahakaruna—and it is this that we break down into me, you, we, doing stuff to things, and making things happen.