Many suttas have been badly mistranslated due to a lack of understanding of key concepts on the part of the translator.
The passage that you quoted should be translated as :
“Bhikkhus, if wanderers who follow another path were to ask you: ‘Reverends, what was the ascetic Gotama’s usual meditation during the rainy season residence?’ You should answer them like this. ‘Reverends, the ascetic Gotama’s usual meditation during the rainy season residence was immersion in Anapanasati.”
Translating Anapanasati as “breath meditation” is a serious error.
– Translating bhikkhu as a “mendicant” or a “beggar” is a serious error too.
Engaging in Anapanasati is to contemplate the anicca, dukkha, anatta nature of this world. Alternatively, it is also “taking in the eightfold path” and “discarding the opposite (miccha ditthi through miccha samadhi)”.
– For those on the Noble path (those who have understood the meaning) that would make them progress on the Path towards various magga phala and eventually to Arahanthood.
– For those who have already attained Arahanthood (or the Buddhahood), as well as those who are still on the Noble Path, it also leads to a pleasant state of mind (including jhanic experiences).
That last point may raise questions. If the Buddha (or an Arahant) has already discarded the opposites of the Noble Path Factors, then why do they need to engage in Anapanasati?
– Because that provides relief to the mind.
– Even Arahants have “agitation of the mind” (NOT defilements) due to kamma vipaka. They also have bodily dukkha/sukha vedana due to kamma vipaka as everyone else.
– There are several suttas that state clearly that contemplation of Tilakkhana is advised for all, including Arahants.
Engaging in Anapanasati is also referred to as “Brahama vihara” in several suttas, including the Karaniyamatta Sutta. “Karaniya Metta Sutta – Metta Bhavana”
– Dealing with average humans causes distress in the mind, even for a Buddha. One time, some bhikkhus started breaking up into two factions and when he could not get them to settle the dispute, the Buddha went into the forest and spent some time by himself.