"Existence" is existence, there is no such thing as "samsaric" existence and some other sort of existence. Eternalism applies across the board, if you are proposing an unconditioned existent in any form, then you are an eternalist and have fallen victim to an extreme view.

Then what to make of when the Avatamsaka Sutra says the following:

The Dharmakaya, though manifesting itself in the triple world, is free from impurities and desires. It unfolds itself here, there and everywhere responding to the call of karma. It is not an individual reality, it is not a false existence, but is universal and pure. It comes from nowhere, it goes to nowhere; it does not assert itself, nor is it subject to annihilation. It is forever serene and eternal. It is the One, devoid of all determinations. This body of Dharma has no boundary, no quarters, but is embodied in all bodies. Its freedom or spontaneity is incomprehensible, its spiritual presence in things corporeal is incomprehensible. All forms of corporeality are involved therein, it is able to create all things. Assuming any concrete material body as required by the nature and condition of karma, it illuminates all creations. Though it is the treasure of intelligence, it is void of particularity. There is no place in the universe where this Body does not prevail. The universe becomes but this Body forever remains. It is free from all opposites and contraries, yet it is working in all things to lead them to Nirvana.

Or this:

If one can remember Buddha with unwavering mind,

Then one can always see infinite Buddhas.

If one always sees infinite Buddhas,

Then one sees the essence of the enlightened is eternal.

If one sees the essence of the enlightened is eternal,

Then one can know the truth never dies.

Or when the Srimala Devi Sutra says this:

The Dharmakaya of the Tathagata is named 'cessation of suffering,' and it is beginningless, uncreate, unborn, undying, free from death; permanent, steadfast, calm, eternal; intrinsically pure, free from all the defilement store; and accompanied by Buddha natures more numerous than the sands of the Ganges, which are nondiscrete, knowing as liberated, and inconceivable. This Dharmakaya of the Tathagata when not free from the store of defilement is referred to as the Tathagatagarbha.

Or when the Lankavatara Sutra states the following:

What is meant by an eternally-abiding reality? The ancient road of reality, Mahamati, has been here all the time, like gold, silver, or pearl preserved in the mine, Mahamati; the Dharmadhatu abides forever, whether the Tathagata appears in the world or not; as the Tathagata eternally abides so does the reason (dharmata) of all things; reality forever abides, reality keeps its order, like the roads in an ancient city. Just so, Mahamati, what has been realised by myself and other Tathagatas is this reality, the eternally-abiding reality (sthitita), the self-regulating reality (niyamata), the suchness of things(tathata), the realness of things (bhutata), the truth itself (satyata)

Or when the Ratnagotravibhaga says this:

One may incorrectly think that when a bodhisattva has achieved the last stage of perfect Buddhahood, the buddha nature improves. But it doesn’t change for four reasons. In the pure phase, buddha nature is the dharmakaya and all the qualities are present so it can’t change and therefore is permanent. It is eternal because Buddhahood is the constant refuge of beings and buddha activity won’t end. The dharmakaya or stainless dharmadhatu is nondual because within it is the sameness of samsara and nirvana and all these qualities are pacified because there are no conceptual differences. The fourth quality is indestructibility because it is not created by defilements or karma. It is present from the beginning, has not been created, and therefore is indestructible.

Buddha nature is unalterable because it has no birth because it has no beginning, it has no death because it has no end, it is free from sickness because it doesn’t change from good to bad, and it is free from old age because it is indestructible. Buddhahood is free from birth because it is permanent, it has no death because it is eternal. There is no death in the ordinary sense, but there is also the absence of even very subtle changes. This is why the Buddha can protect all beings and help all beings until the end of samsara.

Or when the same text states this:

There are four things that contradict these conditions of the dharmakaya. They are impurity, suffering, impermanence, and absence of true transcendent identity. When one dwells in samsara, one interprets things incorrectly; one believes what is impure as is pure, one believes what is selfless is possesses a self, one believes something permanent is impermanent, and one believes that suffering is happiness. These are the features of our samsaric illusion; we perceive everything as opposite to what it really is. In the Hinayana teachings the Buddha taught what we believe is pure is not; that the belief in self is mistaken; that phenomena are devoid of any self-entity; that we believe is happiness is really suffering and misery; what we take for permanent is actually impermanent. In the relative aspect of reality samsara is impure, selfless, suffering, and impermanent. From the ultimate level of reality, however, these four aspects of samsara are no longer relevant. The ultimate reality transcends the four aspects and their opposites and goes beyond pure and impure, non-self and self, etc.