How or why do arahants not experience aging & death?

A sage at peace is not born, does not age, does not die, is unagitated, and is free from longing. He has nothing whereby he would be born. Not being born, will he age? Not aging, will he die? Not dying, will he be agitated? Not being agitated, for what will he long? It was in reference to this that it was said, 'He has been stilled where the currents of construing do not flow. And when the currents of construing do not flow, he is said to be a sage at peace.' MN 140

Here, I think the Buddha is telling that an arahant wouldn’t be born in future lives. Therefore, there will be no aging. When there is no birth and aging there will be no death.

Arahants don’t experience aging and death in this because they know that only their body is aging. Their body still age but they don’t assume the body to be “me” or “them” because they have cut off all fetters.

The sage at peace is not reborn, does not grow old, and does not die. They are not shaken, and do not yearn. For they have nothing which would cause them to be reborn. Not being reborn, how could they grow old? Not growing old, how could they die? Not dying, how could they be shaken? Not shaking, for what could they yearn? ‘They have four foundations, standing on which the streams of conceit don’t flow. And when the streams of conceit don’t flow, they’re called a sage at peace.’ That’s what I said, and this is why I said it. Mendicant, you should remember this brief analysis of the six elements.” https://suttacentral.net/mn140/en/sujato

Here, it said a sage is not reborn

That's the problem when refusing to accept regrouping of 5 skandhas after breaking up of this body. Many suttas will not make sense , either you will have to dismiss large part of it or do an acrobatic twist of the scriptures to fit your views. Such as the obvious maximum reappearing of stream enteres 7 lives the most, you twisted into 7 fetters . When challenge with once returners or non-returner, .how is that compared to fetters, you couldn't twist it further. You don't believe in reappearing after death but you shouldn't twist Buddha's words to match your views . According to that idea, everyone reaches nirvana at the end no matter what.
Well , to answer ur question , Arahats dont age anymore because there will be no regrouping for them when this group is broken. As far as current body, they do age. Remember a sutta when ven Ananda comment on Buddha's wrinkles and slight hunch of the back. .

Arahants experience ageing and death but do not suffer from it, after attaining Nibbana.

From DN 16:

"Now I am frail, Ananda, old, aged, far gone in years. This is my eightieth year, and my life is spent. Even as an old cart, Ananda, is held together with much difficulty, so the body of the Tathagata is kept going only with supports. It is, Ananda, only when the Tathagata, disregarding external objects, with the cessation of certain feelings, attains to and abides in the signless concentration of mind, that his body is more comfortable.

Experience of sensations continue to occur for arahants till their parinibbana, as stated in Iti 44:

And what is the Unbinding property with fuel remaining? There is the case where a monk is an arahant whose fermentations have ended, who has reached fulfillment, finished the task, laid down the burden, attained the true goal, ended the fetter of becoming, and is released through right gnosis. His five sense faculties still remain and, owing to their being intact, he is cognizant of the agreeable & the disagreeable, and is sensitive to pleasure & pain. His ending of passion, aversion, & delusion is termed the Unbinding property with fuel remaining.

And what is the Unbinding property with no fuel remaining? There is the case where a monk is an arahant whose fermentations have ended, who has reached fulfillment, finished the task, laid down the burden, attained the true goal, ended the fetter of becoming, and is released through right gnosis. For him, all that is sensed, being unrelished, will grow cold right here. This is termed the Unbinding property with no fuel remaining."

Commentary (Thanissaro):
With fuel remaining (sa-upadisesa) and with no fuel remaining (anupadisesa): The analogy here is to a fire. In the first case, the flames are out, but the embers are still glowing. In the second, the fire is so thoroughly out that the embers have grown cold. The "fuel" here is the five aggregates. While the arahant is still alive, he/she still experiences the five aggregates, but they do not burn with the fires of passion, aversion, or delusion. When the arahant passes away, there is no longer any experience of aggregates here or anywhere else.

But what does it mean when we say that Arahants become deathless? This is because of Nibbana, suffering ends, birth ends and so death also ends.

From Dhammapada 400:

Akkodhanam vatavantam
silavantam anussadam
dantam antimasariram¹
tamaham brumi brahmanam

Verse 400: Him I call a brahmana, who is free from anger, who practises austerity, who is virtuous and free from craving, who is controlled in his senses and for whom this body (i.e., existence) is the very last.

Footnote 1. antimasariram: lit., one who has the last body. This is his last body because he will not be reborn; he is an arahat.

But how does the Arahant become free from suffering and death? As we know from the third noble truth, suffering is ceased when craving is ceased. The requisite condition for ageing and death is birth.

From SN 44.9:

And at the moment when a being sets this body aside and is not yet reborn in another body, what do you designate as its sustenance then?"

"Vaccha, when a being sets this body aside and is not yet reborn in another body, I designate it as craving-sustained, for craving is its sustenance at that time."