I believe that the steps in the APS map to the jhana states as you have outlined here. I’ve been working to prepare a study guide for APS that is available here:
(you are welcome to provide feedback or suggest edits)
I noted in reviewing different texts the following: Some suggests that jhana occurs in the fourth contemplation of the kaya tetrad, see [Buddhadasa Bhikkhu. Anapanasati: Mindfulness of Breathing. Translated by Bhikkhu Nagasena, Sublime Life Mission, 1976. Others mention that the Jhana states occur later at the fourth contemplation of the citta tetrad (Ajahn Brahm) or the third contemplation of the citta tetrad ([Bhikkhu Nanamoli. Mindfulness of Breathing: Ánápánasati. Buddhist Publication Society, Kandy, 2010). Thus, there is quite a diversity of opinion on this matter.
Lately, I’ve also been wondering about the four arupa (formless) jhanas:
The four arupas are:
- fifth jhāna: infinite space (Pali ākāsānañcāyatana , Skt. ākāśānantyāyatana ),
- sixth jhāna: infinite consciousness (Pali viññāṇañcāyatana , Skt. vijñānānantyāyatana ),
- seventh jhāna: infinite nothingness (Pali ākiñcaññāyatana , Skt. ākiṃcanyāyatana ),
- eighth jhāna: neither perception nor non-perception (Pali nevasaññānāsaññāyatana , Skt. naivasaṃjñānāsaṃjñāyatana ).
The four dhamma tetrad items are:
- Dwelling on impermanence
- Dwelling on dispassion ( virāga ). SA 8.10 instead has ‘eradication’.
- Dwelling on cessation ( nirodha ). SA 8.10 instead has ‘dispassion’.
- Dwelling on relinquishment ( paṭinissaggā ). SA 8.10 instead has ‘cessation’.
I wonder if these could parallel the four steps in the dhamma tetrad. This might be a bit of a stretch to try to make a 1:1 correspondence, but I feel that when reflecting on the dhamma tetrad, one’s mind expands and seems to enter these arupa jhana-like states to varying degrees.