SN22.85/SA104 doesn’t indeed say there is a ‘spiritual atta’, or whatever else there is. It simply says there is no atta inside the aggregates and no atta besides them -thereby concretely analytically ruling out there being an atta anywhere at all. Yamaka’s mistaken view was that there was an atta before and after death there will be no atta, and the Buddha proves to him that even now there is no atta (in the aggregates, or even outside the aggregates). Yamaka had been unwilling to give up his wrong view, hence the Buddha having to intercede and explain it to him.
Why do you say: ‘[As] I understand the Dharma taught by the Buddha, an arahant, with the influxes being eradicated, will not exist anywhere after the body breaks up at the end of life’? Is that properly spoken?”
[Yamaka] replied: “No, venerable Sāriputta.” SA104
So the correct way to say it is…
Sāriputta] asked again: “Yamaka, if you are further asked: ‘Monk, as you earlier declared an evil wrong view, knowing and seeing what has this now all been completely removed?’ What would you answer?”
Yamaka replied: “Venerable Sāriputta, if someone comes and asks, I would answer in this way: ‘The bodily form of an arahant, with the influxes being eradicated, is impermanent. What is impermanent, is dukkha . What is dukkha has become tranquil and become cool, it has forever disappeared. Feeling, perception … formations … consciousness is also like this.’ [If] someone comes and asks, I would answer in this way.”
Sāriputta said: “It is well, it is well, monk Yamaka. You should answer in this way. Why is that? The bodily form of an arahant, with the influxes being eradicated, is impermanent.
Dukkha arises, dukkha passes away.