The CRITICAL point that I have been trying to convey is that translating “Ānāpānassati” as “mindfulness of breathing” is INCORRECT!
I have revised #5 of that post as follows.
5. There is a small collection of suttas in the Ānapāna Vagga of Saṁyutta Nikāya BEFORE the section on Ānāpānasati. That is to give an idea of what is involved in Ānapāna, which comes from “Āna” + “āpāna,” where two words mean “taking in (kusala)” and “discarding (akusala or defilements).”
– That section in the Ānapāna Vagga has several suttas starting with the “Aṭṭhikamahapphala Sutta (SN 46.57)” and ending with the “Ānāpāna Sutta (SN 46.66).”
– You can read the English translations in the above links and see that the word “breath” is NOT there! Of course, the INCORRECT English translation of “Ānāpānassati” as “mindfulness of breathing” in SN 46.66 does not mean the word “breathing” is mentioned in that sutta! That INCORRECT translation is in the Sutta Central translation in the above link. (Note: I usually provide the “side by side” Pāli and English translations from Sutta Central. That does NOT mean I agree with their translation. One should always be cautious about the INCORRECT translation of many words in Sutta Central translations).