It's wrong translation.
"tesaṁ tesaṁ sattānaṁ" is chatthi-vibhatti (of), not catutthi-vibhatti (for). So, it is "Yā (jāti) tesaṁ tesaṁ sattānaṁ (of the various beings)", it is not "Yā (jāti) tesaṁ tesaṁ sattānaṁ (for the various beings)". It's like "your birth" is not "for birth".
The subject of the sentence is "Yā ... jāti sañjāti okkanti abhinibbatti, khandhānaṁ pātubhāvo, āyatanānaṁ paṭilābho". The subject is not satta. It means the Buddha is focusing on describing dhamma (things which assembled then called Satta) in this sentence as same as in AbhidhammaNaya.
The Subjective Complement of "Yā" is "tesaṁ tesaṁ sattānaṁ tamhi tamhi sattanikāye". It means Yā-jāti-...-yā-āyatanānaṁ-paṭilābho of (what is called) satta who living surrounded by sattanikāya.
So the whole sentence in SuttantaNaya is the same in AbhidhammaNaya as...
What is the thing of the various beings (sattanam) who living surrounded by sattanikāya is called "bhavapaccayā jāti"? The thing is called "birth thing, being born thing, appearing thing, arising thing, turning up thing, the manifestation of the constituents thing (of mind and bodily form), the acquisition of the sense spheres thing" is what is called "bhavapaccayā jāti".
Tattha katamā bhavapaccayā jāti? 17.2Yā tesaṁ tesaṁ sattānaṁ tamhi tamhi sattanikāye jāti sañjāti okkanti abhinibbatti, khandhānaṁ pātubhāvo, āyatanānaṁ paṭilābho— 17.3ayaṁ vuccati “bhavapaccayā jāti”.
But because "tesaṁ tesaṁ sattānaṁ tamhi tamhi sattanikāye" is not the subject of the question because the question is about the thing. It is the question inside the dependent origination and suffering noble truth for the right view of eight noble path. It must be only thing, not Satta. So, "tesaṁ tesaṁ sattānaṁ tamhi tamhi sattanikāye" is not included in the question part, but it is The Subjective Complement of the answer part ot show "Satto is unreal. It is only thing arising and vanishing".
Are there any Suttas referring to the "jati" of "things" rather than the "jati" of "beings" in relation to dependent origination?
There are uncountable Suttas. For the example:
kenāyaṃ pakato satto kvaci 1- sattassa kārako
kvaci 2- satto samuppanno kvaci 3- satto nirujjhatīti.
kiṃ nu sattoti pacceti 4- māra diṭṭhigataṃ nu te
suddhasaṅkhārapuñjo yaṃ nayidha sattupalabbhati
yathā hi aṅgasambhārā hoti saddo ratho iti
evaṃ khandhesu santesu hoti sattoti sammati 5-
By whom has this being been created?
Where is the maker of the being?
Where has the being arisen?
Where does the being cease?
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.
Life is easy if we open our view to learn.