Does "abhinibbatti" mean "reincarnation" in the Pali suttas?

1. In the first chapter of the first canon of tipiṭaka, Vinaya verañjakaṇḍa and Sutta. Aṅ. (4): sattaka-aṭṭhaka-navakanipātā Mahāvaggo Dutiyo verañjasutta, already show all of them: jāti, sañjāti, abhinibbatti, khandhānaṃ pātubhāvo.
2. And for āyatanānaṃ paṭilābho and okkanti, it appears in Sutta. Tī. Pā. Saṅgītisuttaṃ.
3. There are many sutta about rebirth in Sutta such as SN Khandhavagga Nāgasamyutta, etc.

Let's see:

1. jāti, sañjāti, abhinibbatti, khandhānaṃ pātubhāvo in verañjakaṇḍa

Abhinibbatti is rebirth into the wombs:

The Realized One has given up future wombs, which is rebirth (abhinibbatti) into a new state of existence. He has cut them off at the root, made them like a palm stump, exterminated them, so that they’re unable to arise in the future.

Tathāgatassa kho, brāhmaṇa, āyatiṃ gabbhaseyyā (=each other synonym=) punabbhavābhinibbatti pahīnā ucchinnamūlā tālāvatthukatā anabhāvaṅkatā āyatiṃ anuppādadhammā.

and

This was my first breaking out, like a chick breaking out of the eggshell.

Ayaṃ kho me, brāhmaṇa, paṭhamā abhinibbhidā ahosi kukkuṭacchāpakasseva aṇḍakosamhā. (1)

The others synonyms and the other related words, such as maraṇa cuti bheda, are used as the bold words below:

“There is, brahmin, a sense in which you could rightly say that

“Atthi khvesa, brāhmaṇa, pariyāyo, yena maṃ pariyāyena sammā vadamāno vadeyya:

I’m an abortionist.

‘apagabbho samaṇo gotamo’ti.

I say that an abortionist is someone who has given up future wombs and rebirth into a new state of existence. They’ve cut them off at the root, made them like a palm stump, exterminated them, so that they’re unable to arise in the future.

Yassa kho, brāhmaṇa, āyatiṃ gabbhaseyyā punabbhavābhinibbatti pahīnā ucchinnamūlā tālāvatthukatā anabhāvaṅkatā āyatiṃ anuppādadhammā, tamahaṃ ‘apagabbho’ti vadāmi.

The Realized One has given up future wombs and rebirth into a new state of existence. He has cut them off at the root, made them like a palm stump, exterminated them, so that they’re unable to arise in the future.

Tathāgatassa kho, brāhmaṇa, āyatiṃ gabbhaseyyā punabbhavābhinibbatti pahīnā ucchinnamūlā tālāvatthukatā anabhāvaṅkatā āyatiṃ anuppādadhammā.

In this sense you could rightly say that I’m an abortionist.

Ayaṃ kho, brāhmaṇa, pariyāyo, yena maṃ pariyāyena sammā vadamāno vadeyya:

But that’s not what you’re talking about.

‘apagabbho samaṇo gotamo’ti, no ca kho yaṃ tvaṃ sandhāya vadesi. (8)

...

When my mind had immersed in samādhi like this—purified, bright, spotless, rid of taints, pliable, workable, steady, and imperturbable—I extended it toward recollection of past lives.

So evaṃ samāhite citte parisuddhe pariyodāte anaṅgaṇe vigatūpakkilese mudubhūte kammaniye ṭhite āneñjappatte pubbenivāsānussatiñāṇāya cittaṃ abhininnāmesiṃ.

I recollected many kinds of past lives. That is: one, two, three, four, five, ten, twenty, thirty, forty, fifty, a hundred, a thousand, a hundred thousand rebirths; many eons of the world contracting, many eons of the world evolving, many eons of the world contracting and evolving. I remembered: ‘There, I was named this, my clan was that, I looked like this, and that was my food. This was how I felt pleasure and pain, and that was how my life ended. When I passed away from that place I was reborn somewhere else. There, too, I was named this, my clan was that, I looked like this, and that was my food. This was how I felt pleasure and pain, and that was how my life ended. When I passed away from that place I was reborn here.’ And so I recollected my many kinds of past lives, with features and details.

So anekavihitaṃ pubbenivāsaṃ anussarāmi, seyyathidaṃ—ekampi jātiṃ dvepi jātiyo tissopi jātiyo catassopi jātiyo pañcapi jātiyo dasapi jātiyo vīsampi jātiyo tiṃsampi jātiyo cattālīsampi jātiyo paññāsampi jātiyo jātisatampi jātisahassampi jātisatasahassampi anekepi saṃvaṭṭakappe anekepi vivaṭṭakappe anekepi saṃvaṭṭavivaṭṭakappe: ‘amutrāsiṃ evaṃnāmo evaṅgotto evaṃvaṇṇo evamāhāro evaṃsukhadukkhappaṭisaṃvedī evamāyupariyanto. So tato cuto (=maraṇa) amutra udapādiṃ; tatrāpāsiṃ evaṃnāmo evaṅgotto evaṃvaṇṇo evamāhāro evaṃsukhadukkhappaṭisaṃvedī evamāyupariyanto. So tato cuto idhūpapanno’ti. Iti sākāraṃ sauddesaṃ anekavihitaṃ pubbenivāsaṃ anussarāmi.

This was the first knowledge, which I achieved in the first watch of the night.

Ayaṃ kho me, brāhmaṇa, rattiyā paṭhame yāme paṭhamā vijjā adhigatā;

Ignorance was destroyed and knowledge arose; darkness was destroyed and light arose, as happens for a meditator who is diligent, keen, and resolute.

avijjā vihatā vijjā uppannā; tamo vihato āloko uppanno, yathā taṃ appamattassa ātāpino pahitattassa viharato.

This was my first breaking out, like a chick breaking out of the eggshell.

Ayaṃ kho me, brāhmaṇa, paṭhamā abhinibbhidā ahosi kukkuṭacchāpakasseva aṇḍakosamhā. (1)

When my mind had immersed in samādhi like this—purified, bright, spotless, rid of taints, pliable, workable, steady, and imperturbable—I extended it toward knowledge of the death and rebirth of sentient beings.

So evaṃ samāhite citte parisuddhe pariyodāte anaṅgaṇe vigatūpakkilese mudubhūte kammaniye ṭhite(ṭhiti) āneñjappatte sattānaṃ cutūpapātañāṇāya(cuti/cavanatā[maraṇa] + upapāta > pātubhāva) cittaṃ abhininnāmesiṃ.

With clairvoyance that is purified and superhuman, I saw sentient beings passing away and being reborn—inferior and superior, beautiful and ugly, in a good place or a bad place. I understood how sentient beings are reborn according to their deeds: ‘These dear beings did bad things by way of body, speech, and mind. They spoke ill of the noble ones; they had wrong view; and they acted out of that wrong view. When their body breaks up, after death, they’re reborn in a place of loss, a bad place, the underworld, hell. These dear beings, however, did good things by way of body, speech, and mind. They never spoke ill of the noble ones; they had right view; and they acted out of that right view. When their body breaks up, after death, they’re reborn in a good place, a heavenly realm.’ And so, with clairvoyance that is purified and superhuman, I saw sentient beings passing away and being reborn—inferior and superior, beautiful and ugly, in a good place or a bad place. I understood how sentient beings are reborn according to their deeds.

So dibbena cakkhunā visuddhena atikkantamānusakena satte passāmi cavamāne upapajjamāne hīne paṇīte suvaṇṇe dubbaṇṇe, sugate duggate yathākammūpage satte pajānāmi: ‘ime vata bhonto sattā kāyaduccaritena samannāgatā, vacīduccaritena samannāgatā, manoduccaritena samannāgatā, ariyānaṃ upavādakā, micchādiṭṭhikā, micchādiṭṭhikammasamādānā. Te kāyassa bhedā paraṃ maraṇā apāyaṃ duggatiṃ vinipātaṃ nirayaṃ upapannāti. Ime vā pana bhonto sattā kāyasucaritena samannāgatā, vacīsucaritena samannāgatā, manosucaritena samannāgatā, ariyānaṃ anupavādakā, sammādiṭṭhikā, sammādiṭṭhikammasamādānā. Te kāyassa bhedā paraṃ maraṇā sugatiṃ saggaṃ lokaṃ upapannā’ti. Iti dibbena cakkhunā visuddhena atikkantamānusakena satte passāmi cavamāne upapajjamāne hīne paṇīte suvaṇṇe dubbaṇṇe, sugate duggate yathākammūpage satte pajānāmi.

This was the second knowledge, which I achieved in the middle watch of the night.

Ayaṃ kho me, brāhmaṇa, rattiyā majjhime yāme dutiyā vijjā adhigatā;

Ignorance was destroyed and knowledge arose; darkness was destroyed and light arose, as happens for a meditator who is diligent, keen, and resolute.

avijjā vihatā vijjā uppannā; tamo vihato āloko uppanno, yathā taṃ appamattassa ātāpino pahitattassa viharato.

This was my second breaking out, like a chick breaking out of the eggshell.

Ayaṃ kho me, brāhmaṇa, dutiyā abhinibbhidā ahosi kukkuṭacchāpakasseva aṇḍakosamhā. (2)

...

When it was freed, I knew ‘it is freed’.

Vimuttasmiṃ vimuttamiti ñāṇaṃ ahosi.

I understood: ‘Rebirth is ended; the spiritual journey has been completed; what had to be done has been done; there is no return to any state of existence.’

‘Khīṇā jāti, vusitaṃ brahmacariyaṃ, kataṃ karaṇīyaṃ, nāparaṃ itthattāyā’ti abbhaññāsiṃ.

This was the third knowledge, which I achieved in the last watch of the night.

Ayaṃ kho me, brāhmaṇa, rattiyā pacchime yāme tatiyā vijjā adhigatā;

Ignorance was destroyed and knowledge arose; darkness was destroyed and light arose, as happens for a meditator who is diligent, keen, and resolute.

avijjā vihatā vijjā uppannā; tamo vihato āloko uppanno, yathā taṃ appamattassa ātāpino pahitattassa viharato.

This was my third breaking out, like a chick breaking out of the eggshell.”

Ayaṃ kho me, brāhmaṇa, tatiyā abhinibbhidā ahosi kukkuṭacchāpakasseva aṇḍakosamhā”ti. (3)

2. āyatanānaṃ paṭilābho and okkanti in Saṅgītisuttaṃ

Four kinds of conception.

Catasso gabbhāvakkantiyo.

Someone is unaware when conceived in their mother’s womb, unaware as they remain there, and unaware as they emerge. This is the first kind of conception.

Idhāvuso, ekacco asampajāno mātukucchiṃ okkamati, asampajāno mātukucchismiṃ ṭhāti, asampajāno mātukucchimhā nikkhamati, ayaṃ paṭhamā gabbhāvakkanti.

...

Four kinds of reincarnation.

Cattāro attabhāvapaṭilābhā.

There is a reincarnation where only one’s own intention is effective, not that of others.

Atthāvuso, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe attasañcetanāyeva kamati, no parasañcetanā.

...