DN 16, MN 8 Buddha and Alara not hearing sounds from 500 carts and thunderstorm is 'peaceful dwelling', not 'four jhānas'

I found a nice contrast between 'peaceful dwelling' and 'pleasant dwelling' of four jhānas in MN 8.

hearing in jhāna👂🌄 : You can hear sounds in the 4 jhānas. Which samādhis are silent?

'Santa Vihara', Peaceful dwellings, are formless attainments, not 4 jhānas

Besides the imperturbable formless samādhi where one can not hear sounds, the another term that is used is 'Santa Vihara', Peaceful dwellings.
In DN 16 when Buddha and his Teacher can not hear sounds, they are in Santa Vihara.
As MN 8 very clearly delineates, the four jhānas are 'pleasant dwellings', as opposed to the 4 formless attainments which are 'peaceful dwellings.'

● MN 8 - 🔗🔊 22.5m, Sallekha: self effacement

     MN 8⁰ (Many wrong views on self and world)
        MN 8^0.3 (how to give up those wrong views? Seeing not mine, not self...)
        MN 8^0.8.1 (1st jhāna... 4th jhāna is pleasant dwelling, not self-effacement)
        MN 8^0.8.5 (dimension of infinite space... neither perception nor non, is peaceful dwelling, not self-effacement)
    MN 8¹ (Sallekhapariyāya: The Exposition of Self-Effacement, list 44 ways)
    MN 8² (Cittupapādapariyāya: Giving Rise to the Thought)
    MN 8³ (Parikkamanapariyāya: A Way Around)
    MN 8⁴ (Uparibhāgapariyāya: Going Up)
    MN 8⁵ (Pari-nibbāna-pariyāya: The Exposition by Nirvana)
        MN 8^5.3 (if you’re not nirvana’d you can’t liberate others ↔ if you stuck in mud, can’t pull out others)

DN 16 Buddha was in formless samādhi when he couldn't hear, not four jhānas as Brahm and Vism. wrongly claim

‘Idāni, bhante, deve vassante deve gaḷagaḷāyante vijjullatāsu niccharantīsu asaniyā phalantiyā	‘Just now, sir [Buddha], it was raining and pouring, lightning was flashing, and thunder was cracking.
dve kassakā bhātaro hatā cattāro ca balibaddā.	And two farmers who were brothers were killed, as well as four oxen.
Ettheso mahājanakāyo sannipatito.	Then this crowd gathered here.
Tvaṃ pana, bhante, kva ahosī’ti?	But sir, where were you?’
‘Idheva kho ahaṃ, āvuso, ahosin’ti.	‘I was right here, friend.’
‘Kiṃ pana, bhante, addasā’ti?	‘But sir, did you see?’
‘Na kho ahaṃ, āvuso, addasan’ti.	‘No, friend, I didn’t see anything.’
‘Kiṃ pana, bhante, saddaṃ assosī’ti?	‘But sir, didn’t you hear a sound?’
‘Na kho ahaṃ, āvuso, saddaṃ assosin’ti.	‘No, friend, I didn’t hear a sound.’
‘Kiṃ pana, bhante, sutto ahosī’ti?	‘But sir, were you asleep?’
‘Na kho ahaṃ, āvuso, sutto ahosin’ti.	‘No, friend, I wasn’t asleep.’
‘Kiṃ pana, bhante, saññī ahosī’ti?	‘But sir, were you conscious?’
‘Evamāvuso’ti.	‘Yes, friend.’
‘So tvaṃ, bhante, saññī samāno jāgaro deve vassante deve gaḷagaḷāyante vijjullatāsu niccharantīsu asaniyā phalantiyā neva addasa, na pana saddaṃ assosī’ti?	‘So, sir, while conscious and awake you neither saw nor heard a sound as it was raining and pouring, lightning was flashing, and thunder was cracking?’
‘Evamāvuso’ti?	‘Yes, friend.’
Atha kho, pukkusa, tassa purisassa etadahosi:	Then that person thought:
‘acchariyaṃ vata bho, abbhutaṃ vata bho, santena vata bho pabbajitā vihārena viharanti.	‘It’s incredible, it’s amazing! Those who have gone forth remain in such peaceful meditations,
Yatra hi nāma saññī samāno jāgaro deve vassante deve gaḷagaḷāyante vijjullatāsu niccharantīsu asaniyā phalantiyā neva dakkhati, na pana saddaṃ sossatī’ti.	in that, while conscious and awake he neither saw nor heard a sound as it was raining and pouring, lightning was flashing, and thunder was cracking.’