Your question somehow seems to superimpose onto Buddhism the Hindu Advaitin idea of an illusory self merging into God the Ultimate Reality, except that instead of God, you have Nibbana. Buddhism is different.

Eternalism and annihilationism

There is no eternal self. That would be eternalism. If we associate the self with the mental idea of Nibbana, or eternal consciousness or God or Ultimate Reality etc., that would be eternalism, a false view. In MN 38, we read that Sati made this mistake of associating consciousness with the self and assuming it to be eternal or unconditioned.

It is also wrong to say that there is no self at all, or that the self gets destroyed at death or at Nibbana. That would be annihilationism.

Quote from the Acela Sutta (This comes from here but the full text can be found here).

Again, when the Buddha was asked by the naked ascetic Kassapa whether suffering was of one's own making or of another's or both or neither, the Buddha replied "Do not put it like that." When asked whether there was no suffering or whether the Buddha neither knew nor saw it, the Buddha replied that there was, and that he both knew and saw it. He then said "Kassapa, if one asserts that 'He who makes (it) feels (it): being one existent from the beginning, his suffering is of his own making,' then one arrives at eternalism. But if one asserts that one makes (it), another feels (it); being one existent crushed out by feeling, his suffering is of another's making,' then one arrives at annihilationism. Instead of resorting to either extreme a Tathaagata teaches the Dhamma by the middle way (by dependent origination)" (S. XII, 17/vol. ii, 20).

According to the Attakari Sutta, it also doesn't make sense to say that there is no self-doer at all. It is obvious that you can will your hands and legs to move and they will move.

What is the self?

The self is just an idea of the mind that is dependently originated based on conditions and is impermanent. The "birth" (jāti) nidana of dependent origination is the birth of the idea of the self. Snp 4.14 calls this the thought "I am the thinker". This mental idea of the self is reborn from moment to moment i.e. it's changing dependent on conditions.

In the Vina Sutta, we read the analogy of the lute, where different parts of the lute work together to create music. But if you take the lute apart into pieces, you cannot find music. Similarly, the mental idea of the self is constructed by the five aggregates of form, feeling, perception, consciousness and mental formations, by the process of dependent origination. If you take them apart, you cannot find the self. Music here refers to the self (atta), which is what becoming (bhava) and birth (jāti) is about.

According to the Khemaka Sutta, even a stream enterer already fully understands this (i.e. no longer has self-view), but he still has conceit (the self-habit or self-obsession). He KNOWS that "I am the body" or "the body belongs to me" are false views, yet he still FEELS that "I am the body" or "the body belongs to me". That's the difference between self-view and self-habit. Please also see this answer.

In fact, the stream enterer still has seven of the ten fetters. The non-returner would still have all the higher fetters, namely, desire for material existence, desire for immaterial existence, conceit, restlessness and ignorance.

What is Nibbana?

Next, what exactly is Nibbana? It's not an Ultimate Reality or Truth or God.

Nibbana is a mental object to be experienced by the mind. It is that which is experienced by the mind when it is free from defilements.

From this answer, we read:

So, Nibbana is not a thought of the mind, not a concept of the mind, not a state of the mind, not a state of consciousness and also not a feeling. However, when the mind experiences this Nibbana, which is not conditioned, not compounded, not suffering, not impermanent, not arising, not ceasing and not changing, it experiences bliss. The mind can therefore experience Nibbana, but it cannot feel it or think about it.

From AN 9.34:

Ven: Sariputta: “Reverends, Nibbana is bliss!

Ven. Udayi: “But Reverend Sāriputta, what’s blissful about it, since nothing is felt?”

Ven. Sariputta: “The fact that nothing is felt is precisely what’s blissful about it.

Final moment of realization

So, what happened at the final moment of the Buddha's realization?

From MN 36:

“When my concentrated mind was thus purified, bright, unblemished, rid of imperfection, malleable, wieldy, steady, and attained to imperturbability, I directed it to knowledge of the destruction of the taints. I directly knew as it actually is: ‘This is suffering’;…‘This is the origin of suffering’;…‘This is the cessation of suffering’;…‘This is the way leading to the cessation of suffering’;…‘These are the taints’;…‘This is the origin of the taints’;…‘This is the cessation of the taints’;…‘This is the way leading to the cessation of the taints.’

“When I knew and saw thus, my mind was liberated from the taint of sensual desire, from the taint of being, and from the taint of ignorance. When it was liberated there came the knowledge: ‘It is liberated.’ I directly knew: ‘Birth is destroyed, the holy life has been lived, what had to be done has been done, there is no more coming to any state of being.’

“This was the third true knowledge attained by me in the last watch of the night. Ignorance was banished and true knowledge arose, darkness was banished and light arose, as happens in one who abides diligent, ardent, and resolute. But such pleasant feeling that arose in me did not invade my mind and remain.

It's basically the destruction of all ten fetters, the last being ignorance. Ignorance is uprooted by enlightenment, the complete understanding of how it all works. Also uprooted are the underlying tendencies, which are deep-seated habits, hard to be removed.

The buddha became free from rebirth (of the mental idea of the self) and also free from death, i.e. the death of the self. To be deathless, i.e. to not experience the death of the self, because the mental idea of the self is no longer constructed by dependent origination.

When ignorance has been destroyed, craving (a habit of reification) no longer arises from feeling. Without craving, there is no clinging, becoming and birth of the mental idea of the self.

From Khemaka Sutta, we read that the cleaned cloth of the non-returner still has the scent of the self that needs to be finally smoked out, by complete enlightenment:

"Just like a cloth, dirty & stained: Its owners give it over to a washerman, who scrubs it with salt earth or lye or cow-dung and then rinses it in clear water. Now even though the cloth is clean & spotless, it still has a lingering residual scent of salt earth or lye or cow-dung. The washerman gives it to the owners, the owners put it away in a scent-infused wicker hamper, and its lingering residual scent of salt earth, lye, or cow-dung is fully obliterated.

"In the same way, friends, even though a noble disciple has abandoned the five lower fetters, he still has with regard to the five clinging-aggregates a lingering residual 'I am' conceit, an 'I am' desire, an 'I am' obsession. But at a later time he keeps focusing on the phenomena of arising & passing away with regard to the five clinging-aggregates: 'Such is form, such its origin, such its disappearance. Such is feeling... Such is perception... Such are fabrications... Such is consciousness, such its origin, such its disappearance.' As he keeps focusing on the arising & passing away of these five clinging-aggregates, the lingering residual 'I am' conceit, 'I am' desire, 'I am' obsession is fully obliterated."

Parinibbana

Then what is Parinibbana?

Well, there is such a thing as clinging aggregates. According to this answer, for a living arahant, when ignorance is uprooted, this breaks dependent origination, that ends craving, clinging and suffering. In the chain of dependent origination, clinging aggregates would also cease.

The living arahant according to Iti 44, attained nibbana with fuel remaining (sa-upadisesa), meaning the non-clinging aggregates are still functioning like glowing embers, although the fires of passion, aversion and delusion have ceased.

Parinibbana is when the non-clinging aggregates stop functioning. This is nibbana without fuel remaining (anupadisesa) according to Iti 44.

For a living arahant, the music has stopped, but the lute remains. One day, even that will be destroyed. The five clinging aggregates is like a lute vibrating with music, while the five aggregates not subject to clinging is like a silent peaceful lute.

Although I said music, it's more like noise. When the noise stops, you have peace. That's the living arahant's mentally cognized peace of nibbana.

What happens after Parinibbana?

From Yamaka Sutta:

"And so, my friend Yamaka — when you can't pin down the Tathagata as a truth or reality even in the present life — is it proper for you to declare, 'As I understand the Teaching explained by the Blessed One, a monk with no more effluents, on the break-up of the body, is annihilated, perishes, & does not exist after death'?"

"Previously, my friend Sariputta, I did foolishly hold that evil supposition. But now, having heard your explanation of the Dhamma, I have abandoned that evil supposition, and have broken through to the Dhamma."

"Then, friend Yamaka, how would you answer if you are thus asked: A monk, a worthy one, with no more mental effluents: what is he on the break-up of the body, after death?"

"Thus asked, I would answer, 'Form is inconstant... Feeling... Perception... Fabrications... Consciousness is inconstant. That which is inconstant is stressful (suffering). That which is stressful has ceased and gone to its end."

Change of perspective

A change of perspective is needed i.e. rebirth, birth, death, and parinibbana should not be linked to any permanent consciousness or identity. The first noble truth is that there is suffering. It's not there is my suffering or your suffering but simply there is suffering. This also relates to anatta (not self).

Also, think about the core teaching, sabbe dhamma anatta - all phenomena is not self. There is no permanent consciousness or identity or individuality or self in all phenomena.

There is suffering, and it arises because of the mental idea of the self, that arises because the mental idea of the self was constructed by the mind-body phenomena (the five aggregates) through the process of dependent origination, due to ignorance.

Suffering is connected to the mental idea of the self through papanca (reification). This is explained in this answer.

Craving itself is a habit of reification. The self is also a result of reification.

The rebirth of the mental idea of the self from moment to moment is sustained by craving.

When ignorance is uprooted, reification is stopped, craving ceases, which then causes the mental idea of the self to be no longer constructed, and thus suffering is ended.

The key defining feature of the Buddha's enlightenment is not about no more self or no more craving, but rather, no more ignorance. Ignorance is the root of it all.

Please also read SN 12.20 about self-view:

“When, bhikkhus, a noble disciple has clearly seen with correct wisdom as it really is this dependent origination and these dependently arisen phenomena, it is impossible that he will run back into the past, thinking: ‘Did I exist in the past? Did I not exist in the past? What was I in the past? How was I in the past? Having been what, what did I become in the past?’ Or that he will run forward into the future, thinking: ‘Will I exist in the future? Will I not exist in the future? What will I be in the future? How will I be in the future? Having been what, what will I become in the future?’ Or that he will now be inwardly confused about the present thus: ‘Do I exist? Do I not exist? What am I? How am I? This being—where has it come from, and where will it go?’