Does Advaita Vedanta acknowledge the existential reality of suffering and non-suffering occurring in Atman even after the spiritual liberation, or suffering becomes impossible in Atman after the spiritual realization?
‘The existential reality of suffering and non-suffering… in Atman’? You write ‘suffering and non-suffering’, which makes no sense, as written, in the case of the highest principle, Atman (Atman-brahman or the Self) – there cannot be suffering in the Self, only non-suffering. Further, the way the question is written… ‘existential reality’, implies that you have in mind ordinary or worldy experience, but this confuses the issue, since ‘suffering and non-suffering’ cannot be ascribed to either the Self or the (empirical) self (jivatman- seen as individual and separate). Indeed, it is the lot of the self (ego or mind) to be immersed in a sea of difficulties and troubles – opposite ‘realities’ or experiences – but here it is suffering (samsara) what charterizes the life of an ordinary jiva — not ‘non-suffering’.
On self-realization what is eliminated, or, rather, disappears of its own, is psychological suffering – once and for all. No one is mentioning here physical pain, which is a foregone conclusion, as acknowledged by all spiritual traditions – no one more word about this.
One could say more about the cause of suffering by relating it to mind, when the latter (or the ego) is given some reality of its own instead of realizing that it is an illusory superimposition on the Self – all this being an essential doctrine of Advaita Vedanta.