Why is the Pali word 'sattānaṃ' in Dependent Origination plural?

1. Avijjā and saṅkhāra of a past aggregates' rebirth cause a present aggregates' rebirth, present taṅhā&upādāna&kamma-bhava cause a future aggregates' rebirth. So, rebirth is singular is right.

2. It is "each being's rebirth of any beings in any being type".

It's similar to English "one of them go by bus". You can't say "one of him go by A bus".

Yā tesaṃ tesaṃ sattānaṃ (plural) tamhi tamhi sattanikāye (plural) jāti sañjāti okkanti abhinibbatti khandhānaṃ pātubhāvo āyatanānaṃ paṭilābho.

Each (yā) rebirth (jāti) of any (tesaṃ tesaṃ) beings (sattānaṃ) in any (taṃhi taṃhi) being type (sattanikāye) is jāti, sañjāti, okkanti, abhinibbatti (all is the synonym of rebirth), khandhānaṃ pātubhāvo (rebirth of viñnāna&nāma&rūpa in the dependent origination), āyatanānaṃ paṭilābho (the obtaining of saḷāyatanas in the dependent origination because of that rebirth).

I think the answer to his question is found in Wikipedia; however, since Buddhism has become distorted since the Buddha; the Wikipedia answer now falls under Hinduism:

Jāti (in Devanagari: जाति, Bengali: জাতি, Telugu:జాతి, Kannada:ಜಾತಿ, Malayalam: ജാതി, Tamil:ஜாதி, literally "birth") is a group of clans, tribes, communities, and sub-communities, and religions in India. Each Jāti typically has an association with a traditional job function or tribe. Religious beliefs (e.g. Sri Vaishnavism or Veera Shaivism) or linguistic groupings may define some Jātis. A person's surname typically reflects a community (Jāti) association: thus Gandhi = perfume seller, Dhobi = washerman, Srivastava = military scribe, etc.

Wikipedia

Since MN 98 says all differences among human beings are merely "verbal designations" and since SN 23.2 and SN 5.10 say "a being" ('satta') is merely a "view" or "clinging", it appears obvious "birth" ("jati") in Dependent Origination refers to how a single mind gives birth to different views and categories of "people" or "beings".

Also, since the standard teaching of Dependent Origination (in SN 12.2) contains no teachings about "kamma" (such as found in AN 6.63), it is obvious Dependent Origination (in SN 12.2; unlike the dodgy DN 15) is not referring to physical birth as a "human", "god", "animal", "ghost", "hell being", etc.

In short, the reason why "jati" is singular yet "beings" are plural appears to be because "jati" refers to how the individual ignorant mind produces the various views & categories of "people", "beings" or "self-entites".

Examples of these produced "beings within categories of beings" include: good man, bad man, short man, tall man, good woman, bad woman, attractive woman, ugly woman, good monk, bad monks, obese monk, enlightened monk, etc. All of these specific individual beings and the categories or groups of beings they fall into are mind made; made from ignorance.

Note: Only one "being" is produced in each mind moment.

Thich Nhat Hanh provided a clear description of this, when he asked: "What do you call me without a pen?" Answer: "A monk". Then: "what do you call me when you see me drawing calligraphy with a paint brush?" Answer: "A calligrapher". The category of "being" called a "calligrapher" arises from the "appearance or manifestation" of aggregates (khandhānaṃ pātubhāvo) in a different way.

why does 'birth' ('jati'), seemingly a singular process, seem to refer to the multiple births of multiple beings into the multiple orders/groups of beings?

jāti is singular in the passage quoted, so it is not referring to multiple births. sattanikaye is also singular, so "in this or that group of beings".

Why is the plural Pali word 'sattānaṃ' contained in the definition of what appears to be a singular process called 'jati' ('birth') in Dependent Origination?

tesaṃ tesaṃ sattānaṃ is not an ordinary plural, the duplicated pronoun means "of these or those", so the whole phrase means "whatever birth (singular) in this or that being-group of these or those beings".

it were to mean "the multiple births of multiple beings" as you suggest, jāti would have to be plural, which it isn't; yā jāti refers to a singular birth.

The commentary to this clause says:

yā tesaṃ tesaṃ sattānan ti idaṃ “imesaṃ nāmā”ti niyamābhāvato sabbasattānaṃ pariyādānavacanaṃ.

Which I translated roughly as:

yā tesaṃ tesaṃ sattānaṃ: this phrase is the taking up completely of all beings, from not specifying "of these only"

In other words, it is used to make clear that birth is not specific to one or another group of beings, but refers to birth in any group of beings.

In summary, the entire phrase appears simply to be saying that birth refers to any of the many kinds of birth in any of the many groups of beings that exist.