The word 'jati' ('birth') in Dependent Origination actually means a 'self identification', of either 'oneself' or 'others'. For example, about the social identification of a 'bhikkhu', MN 86 says about Aṅgulimāla, the reformed mass murderer:
‘yatohaṁ, bhagini, ariyāya jātiyā jāto, nābhijānāmi sañcicca pāṇaṁ
jīvitā voropetā, tena saccena sotthi te hotu, sotthi gabbhassā’”ti
Ever since I was born in the noble birth, sister, I don’t recall
having intentionally taken the life of a living creature. By this
truth, may both you and your baby be safe.’
MN 86
SN 12.2 defines 'jati' as a 'category of beings (sattanikāye)'. It says:
What is birth?
Katamā ca, bhikkhave, jāti?
Yā tesaṁ tesaṁ sattānaṁ tamhi tamhi sattanikāye jāti sañjāti okkanti
abhinibbatti khandhānaṁ pātubhāvo āyatanānaṁ paṭilābho.
Whatever this & that beings in this & that category/class of beings; their
birth, their co-generation, their emergence, their mental production,
the manifestion/expression of their aggregates, the acquisition/appropriation of
their sense (activity) objects.
SN 12.2 DD translation
Note: 'āyatanā' (sense spheres) above is not 'salāyatanā' (six sense spheres)
For clarification, both SN 23.2 and SN 5.10 define the term 'a being' ('satta') as 'strong attachment' and as 'a conceptual view':
'A being,' lord. 'A being,' it's said. To what extent is one said to
be 'a being'?"
"Any desire, passion, delight, or craving for form, Radha: when one is
caught up there, tied up there, one is said to be 'a being.'
"Any desire, passion, delight, or craving for feeling... perception...
fabrications...
"Any desire, passion, delight, or craving for consciousness, Radha:
when one is caught up there, tied up there, one is said to be 'a
being.
SN 23.2
Why now do you assume 'a being'? Mara, have you grasped a view? This
is a heap of sheer constructions: Here no being is found.
Just as, with an assemblage of parts, The word 'chariot' is used, So,
when the aggregates are present, There's the convention 'a being.'
It's only suffering that comes to be, Suffering that stands and falls
away. Nothing but suffering comes to be, Nothing but suffering ceases.
SN 5.10
The passage in SN 5.10 about 'a being' arising as suffering is found in SN 12.15 about the wrong view of 'my self' arising as suffering:
Does not grasp at it, does not affirm: 'This is my self.' He knows
without doubt or hesitation that whatever arises is merely dukkha that
what passes away is merely dukkha and such knowledge is his own, not
depending on anyone else. This, Kaccaayana, is what constitutes right
view.
SN 12.15
In DN 1, the words 'existent being' and 'self' are used synonymously:
Since this self, good sir, is annihilated and destroyed with the breakup of the body and does not exist after death, at this point the self is completely annihilated.' In this way some proclaim the annihilation, destruction and extermination of an existent being.
DN 1
In Pali, the term 'pubbenivasa' does not mean 'past lives'. It literally means 'past homes; past dwellings; past abodes'. SN 22.79 is the only sutta that unambiguously explains the meaning of 'pubbenivasa', which Bhikkhu Bodhi wisely decided to literally & accurately translate, which also makes it clear a 'pubbenivasa' is when the mind, in the past, ignorantly clung to one or more of the five aggregates as 'self'. SN 22.79 says:
At Savatthi. “Bhikkhus, those ascetics and brahmins who recollect
their manifold past abodes all recollect the five aggregates subject
to clinging or a certain one among them. What five?
“When recollecting thus, bhikkhus: ‘I had such form in the past,’ it
is just form that one recollects. When recollecting: ‘I had such a
feeling in the past,’ it is just feeling that one recollects. When
recollecting: ‘I had such a perception in the past,’ it is just
perception that one recollects. When recollecting: ‘I had such
volitional formations in the past,’ it is just volitional formations
that one recollects. When recollecting: ‘I had such consciousness in
the past,’ it is just consciousness that one recollects.
Therefore, bhikkhus, any kind of form whatsoever … Any kind of feeling
whatsoever … Any kind of perception whatsoever … Any kind of
volitional formations whatsoever … Any kind of consciousness
whatsoever, whether past, future, or present, internal or external,
gross or subtle, inferior or superior, far or near, all consciousness
should be seen as it really is with correct wisdom thus: ‘This is not
mine, this I am not, this is not my self.’
“This is called, bhikkhus, a noble disciple who dismantles and does
not build up; who abandons and does not cling; who scatters and does
not amass; who extinguishes and does not kindle.
“And what is it that he dismantles and does not build up? He
dismantles form and does not build it up. He dismantles feeling …
perception … volitional formations … consciousness and does not build
it up.
“And what is it that he abandons and does not cling to? He abandons
form and does not cling to it. He abandons feeling … perception …
volitional formations … consciousness and does not cling to it.
“And what is it that he scatters and does not amass? He scatters form
and does not amass it. He scatters feeling … perception … volitional
formations … consciousness and does not amass it.
“And what is it that he extinguishes and does not kindle? He
extinguishes form and does not kindle it. He extinguishes feeling …
perception … volitional formations … consciousness and does not kindle
it.
“Seeing thus, bhikkhus, the instructed noble disciple experiences
revulsion towards form, revulsion towards feeling, revulsion towards
perception, revulsion towards volitional formations, revulsion towards
consciousness. Experiencing revulsion, he becomes dispassionate.
Through dispassion his mind is liberated. When it is liberated there
comes the knowledge: ‘It’s liberated.’ He understands: ‘Destroyed is
birth, the holy life has been lived, what had to be done has been
done, there is no more for this state of being.’
SN 22.79
Therefore, while the translations are clunky due to the Pali using the 1st person pronoun, the stock phrase about the First Knowledge found in MN 4 is about what is explained above, namely, billions of 'jatiya' (as found in MN 86) and billions of 'pubbenivasa self views of a being or beings' (as found in SN 22.79). The stock phrase says:
So evaṁ samāhite citte parisuddhe pariyodāte anaṅgaṇe vigatūpakkilese
mudubhūte kammaniye ṭhite āneñjappatte pubbenivāsānussatiñāṇāya cittaṁ
abhininnāmesiṁ. So anekavihitaṁ pubbenivāsaṁ anussarāmi,
When my mind was concentrated like this — purified,
bright, flawless, rid of corruptions, pliable, workable, steady and
imperturbable — I directed it toward recollection of past abodes. I
recollected many various past abodes.
seyyathidaṁ — ekampi jātiṁ dvepi jātiyo tissopi jātiyo catassopi jātiyo
pañcapi jātiyo dasapi jātiyo vīsampi jātiyo tiṁsampi jātiyo
cattālīsampi jātiyo paññāsampi jātiyo jātisatampi jātisahassampi
jātisatasahassampi anekepi saṁvaṭṭakappe anekepi vivaṭṭakappe anekepi
saṁvaṭṭavivaṭṭakappe: ‘amutrāsiṁ evaṁnāmo evaṅgotto evaṁvaṇṇo
evamāhāro evaṁsukhadukkhappaṭisaṁvedī evamāyupariyanto, so tato cuto
amutra udapādiṁ; tatrāpāsiṁ evaṁnāmo evaṅgotto evaṁvaṇṇo evamāhāro
evaṁsukhadukkhappaṭisaṁvedī evamāyupariyanto, so tato cuto
idhūpapanno’ti. Iti sākāraṁ sauddesaṁ anekavihitaṁ pubbenivāsaṁ
anussarāmi.
That is: one, two, three, four, five, ten, twenty, thirty, forty,
fifty, a hundred, a thousand, a hundred thousand births; many time spans
of a world contracting, many time spans of a world expanding, many time spans
of a world contracting and expanding. I remembered: ‘There, this was the name
and clan I had, this was the appearance/expression I had, and that was the
nutriment I had [craved]. This was the pleasure and pain I felt, and that was how a lifeforce (life exertion) i had concluded/reached its limit. When I fell away from that state I originated again.
There, too, I was named this, my clan was that, my appearance was like this,
and that was my nutriment. This was the pleasure and pain I felt, and that
was how a life force [i exerted] concluded/reached its limit/climax. When I fell away from that place I was originated again.’ And so I recollected my [former ignorant mind's] various past abodes [adherences], with their features and details.
Ayaṁ kho me, brāhmaṇa, rattiyā paṭhame yāme paṭhamā vijjā adhigatā,
This was the first knowledge, which I achieved in the first watch of
the night.
avijjā vihatā vijjā uppannā, tamo vihato āloko uppanno, yathā taṁ
appamattassa ātāpino pahitattassa viharato.
Ignorance was destroyed and knowledge arose; darkness was destroyed
and light arose, as happens for a meditator who is diligent, keen, and
resolute.
MN 4 DD translation
Note: SN 12.44 & the end of AN 4.45 explain 'a world' is the arising of a craving becoming.