The formula of SN 26 is:
“Mendicants, the arising, continuation, rebirth, and manifestation of
X is the arising of suffering, the continuation of diseases, and the
manifestation of old age and death.
The cessation of X is the cessation of suffering, the settling of
diseases, and the ending of old age and death.”
If you read the whole of SN 26 (Uppada-samyutta), X refers to eye, ear, nose, tongue, body, mind, sights, sounds, smells, tastes, touches, thoughts, different types of consciousness, different types of contacts, different types of feelings, different types of perceptions, different types of intentions, different types of cravings, the six elements and the five aggregates.
This is just restating "sabbe sankhara dukkha" (Dhammapada 278) or "all conditioned things are suffering" in a longer and more elaborate way, where X = sankhara.
All these conditioned things arise (uppāda), continue (ṭhiti) and reborn (abhinibbatti). These are explained by dependent origination. A "person" or "individual" is compounded and composed of the aforementioned conditioned things. Dependent origination explains the details of how that works.
The fact that they arise (uppāda), continue (ṭhiti) and are reborn (abhinibbatti), would be summarized as their manifestation (pātubhāvo).
Arise here is when the conditioned things arise at birth and continue throughout the moments of life. Rebirth here indeed refers to death and break-up of the body, followed by rearising or rebirth into a new life. Altogether, these stages would represent the manifestation of these conditioned things. The very manifestation of these conditioned things are suffering. This is how it is related to "sabbe sankhara dukkha".
How can I support my opinion that the word "abhinibbatti" indeed refers to "literal" rebirth here? Well, we just need to see how it is used in the other suttas:
In MN 96:
But they are reckoned by recollecting the traditional family lineage
of their mother and father wherever they are incarnated.
panassa mātāpettikaṃ kulavaṃsaṃ anussarato yattha yattheva
attabhāvassa abhinibbatti hoti tena teneva saṅkhyaṃ gacchati.
If they incarnate in a family of aristocrats they are reckoned as an
Khattiyakule ce attabhāvassa abhinibbatti hoti
‘khattiyo’tveva saṅkhyaṃ gacchati;
And as Piya Tan explains for MN 96 here:
Porāṇaṁ kho pan’assa mātā,pettikaṁ kula,vaṁsaṁ anussarato yattha
yatth’eva attabhāvassa abhinibbatti hoti tena ten’eva saṅkhyaṁ
gacchati. “(His) physical rebirth,” attabhāvassa abhinibbatti, lit
“production of selfhood.” Atta,bhāva (BHS ātma,bhāva), bodily form,
body; existence as an individual; living being (V 2:238,17 = A 4:200,6
= 204,2 = 207,2; D 3:111,10; M 2:32,8, 181,11; S 5:442,1; A 1:279,2, 3:411,23; J 4:461,25; Ap 215,11; Miln 171,- 13; Vism 310,27. Often as
~paṭilābha, the becoming; reborn as an individual; reincarnation; type
of body or exist- ence (V 2:185,25 = A 3:122,24; V 3:105,20 = 107,35 =
S 2:255,19; D 3:231,16 = A 2:150,5; M 3:46,6 = 52,33; S 2:272,4,
283,33, 3:144,12); A 2:288,30. While puna-b,bhava (D 2:15; S 1:133,
4:201; Sn 162, 273, 502, 514, 733; It 62) is the term for rebirth as a
cycle, abhinibbatti refers to a particular rebirth, usu in a physical
form (ie a reincarnation) (D 2:305,7 = M 3:249,16 = S 2:3,7 = Vbh
99,14; D 3:94,28): see CPD sv. Also common is punabbhavâbhi- nibbatti,
“rebirth in a new existence” (M 1:294; S 2:65; A 1:225; V 3:3).
Bhikkhu Sujato states here that:
abhinibbatti = rebirth (pretty much only used in this sense)
According to OP:
Bhikkhu Bodhi footnote: 'attabhāvassa abhinibbatti' literally should
be: "wherever the reconception of his individuality takes place"
In the book "Investigating the Dhamma: A Collection of Papers" on page 52, Bhikkhu Bodhi elaborates on this, explaining that "conception" here literally means conception into a new life or new birth:
In fact, the word 'abhinibbatti' is used as one of the synonyms of
jāti in the standard definition of the latter. Apparently when abhinibbatti is included in jāti we should understand jāti as comprising both conception and physical birth, while they are
differentiated, abhinibbatti means conception and jāti is
restricted to full emergence from the womb.