Sakadāgāmi, opapātika, anāgāmi. Are they late concepts i.e. not EBT?

Four Noble Achievements are not later developments.

Just after two years of His Enlightenment, Buddha went to his place of birth. After listening to his discourses, some youth of Sakyans became monks under Him.

"Ānanda… was born on the same day as the Buddha. …When he was 37 years old, joined his brother Anuruddha and his cousin Devadatta and also many other Sakyan nobles to become a “homeless one”, a monk. ( Ānanda, The Guardian of the Dhamma, by Hellmuth Hecker - Buddhist Publication Society, Kandy • Sri Lanka The Wheel Publication No. 273)

Then, from EBT:
Nalakapana Sutta (MN - 68) (Bhikkhu Bodhi Translation)
“Now on that occasion many very well-known clansmen had gone forth out of faith from the home life into homelessness under the Blessed One- the venerable Anuruddha, the venerable Nandiya, the venerable Kimbila, the venerable Bhagu, the venerable Kundadhana, the venerable Revata, the venerable Ananda, and other very well-known…”

(This indicates that this sutta had been delivered to newly ordained monks)

(Following is how he indicates the four Noble Achievements in this same, early sutta)

  1. "Here a bhikkhu hears thus: 'The bhikkhu named so-and- so has died; the Blessed One has declared of him: “He was established in final knowledge.” (An arahant)

  2. "Here a bhikkhu hears thus: 'The bhikkhu named so-and- so has died; the Blessed One has declared of him: “With the destruction of the five lower fetters he has reappeared spontaneously [in the Pure Abodes] and there will attain final Nibbana without ever returning from that world.” (Anāgāmī)

  3. "Here a bhikkhu hears thus: 'The bhikkhu named so-and- so has died; the Blessed One has declared of him: “With the destruction of three fetters and with the attenuation of lust, hate, and delusion, he has become a once-returner, returning once to this world to make an end of suffering.” (sakadāgāmī )

  4. "Here a bhikkhu hears thus: 'The bhikkhu named so-and- so has died; the Blessed One has declared of him: “With the destruction of three fetters he has become a stream-enterer, no longer subject to perdition, bound [for deliverance], headed for enlightenment.” (Sotāpanno)

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How does this intersect with the fifteen, seventeen, or so mind-moments of the path?

The 17 mind-moments themselves are AFAIK Abhidharma, but they, in-turn, are an expansion of the 4 people of the path. How are the 17 moments and the 4 people related, given that Sarvāstivādin Abhidharma has, generally, more of a tendency to follow Suttantā than Theravāda Abhidhamma (if this is true at all)?

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The chart above is actually a study-chart for Abhidharmakośakārikā, so it is like also pulling from this same canon.

Notice the section called Sequence variants in the above Abhidharmakośakārikā chart. It seems to be outlining more or less the same thing you say here, adding substantiation.

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Just wanted to share this bit, maybe it’s new, I don’t know…

AN 6.44 and AN 10.75 have two characters who were reborn in Tusita heaven and were declared Sakadagami by the Buddha. Since Gotama’s last realm was supposedly Tusita too (AN 4.127, AN 8.70, MN 123, DN 14, DN 16), it could mean that the ‘once-’ in once-returner meant that after the human life they could be reborn first in heaven (Tusita) and then being reborn once as humans before arahantship.

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