Any verse in a sutta needs to be analyzed in context. The above verses refer to when our Bodhisatta went through six years of “unfruitful efforts,” subjecting the body to hardships.
Again, it is a good idea to read a sutta with Plai and English side-by-side (keeping in mind that translations of some verses are incorrect). I am linking to emphasize the above point (“Before my awakening”):
“Mahāsaccaka Sutta (MN 36)”
The translation is correct here:
“So I cut off my breathing through my mouth and nose and ears
So kho ahaṁ, aggivessana, mukhato ca nāsato ca kaṇṇato ca assāsapassāse uparundhiṁ.”
– The Bodhisatta was trying a practice implemented by some ascetics to “remove defilements by subjecting the body to hardships.” “assāsapassāsa” in the above verse DOES refer to “breathing in and out.” He was forcefully stopping breathing in and out. This is why it is CRITICAL to note the context. Read the whole sutta, not just specific verses.
But the translation of the first verse you quoted is INCORRECT:
“‘Why don’t I keep practicing the breathless absorption?’
yannūnāhaṁ appāṇakaṁyeva jhānaṁ jhāyeyyan’ti.”
– Here, “jhānaṁ jhāyeyyan’ti” is INCORRECTLY translated as “breathless absorption.”
– As we have discussed, “jhāyi” means to “burn,” specifically to “burn defilements.” The Bodhisatta thought, “Why don’t I try burning defilements (by stop breathing)”?
– See “Jhāna, Jhāya, and Jhāyi – Different Meanings”
This is why it is dangerous to translate (or read) Pali suttas word-by-word without understanding the context!