This answer to my question is "work-in-progress". In other words, I will do more research at a later time. However, my first two contributions are as follows:
Possible explanation #1
Iti 44 distinguishes between two types of Nibbana: (i) still experiencing what is agreeable and disagreeable/ still feeling pleasant and painful feelings (vedana); and (ii) where all that is felt (sabbavedayitāni) grows cold (sīti/sīta). Similar phrases are found in MN 140, which usefully includes a metaphor for explanation but does not include the word "upādisesā", which says:
If he feels a pleasant feeling, he feels it detached; if he feels a painful feeling, he feels it detached; if he feels a neither-painful-nor-pleasant feeling, he feels it detached. When he feels a feeling terminating with the body, he understands: ‘I feel a feeling terminating with the body.’ When he feels a feeling terminating with life, he understands: ‘I feel a feeling terminating with life.’ He understands: ‘On the dissolution of the body, with the ending of life, all that is felt, not being delighted in, will become cool right here.’
Bhikkhu, just as an oil-lamp burns in dependence on oil and a wick, and when the oil and wick are used up, if it does not get any more fuel, it is extinguished from lack of fuel; so too when he feels a feeling terminating with the body… a feeling terminating with life, he understands: ‘I feel a feeling terminating with life.’ He understands: ‘On the dissolution of the body, with the ending of life, all that is felt (sabbavedayitāni), not being delighted in, will become cold (siti) right here.’
Both Iti 44 and particularly MN 140 focus on feelings (vedana). MN 140 uses the literal metaphor of an oil lamp with fuel. In the metaphor, it appears "feeling" is the "burning" of the lamp (rather than the "fuel"). It appears the "fuel" is what is/the things that are felt. In fact, the translation above by Bhikkhu Bodhi appears illogical in terms of the English language. Bhikkhu Sujato's translation appears logical, as follows:
Suppose an oil lamp depended on oil and a wick to burn. As the oil and the wick are used up, it would be extinguished due to lack of
fuel. In the same way, feeling the end of the body approaching, they
understand: ‘I feel the end of the body approaching.’ Feeling the end
of life approaching, they understand: ‘I feel the end of life
approaching.’ They understand: ‘When my body breaks up and my life has
come to an end, everything that’s felt, since I no longer take
pleasure in it, will become cool right here.’
Therefore, the impression from both Iti 44 and MN 140 is "saupādisesā" (fuel/residue remaining) refers to all/the things that are felt, which would be the five aggregates and anything else that are felt.
Possible explanation #2
In AN 7.56, a Brahma God uses the term "saupādisesā" in an explanation to Moggallāna, to which both Moggallāna and the Buddha appear to agree:
But when their body breaks up gods and men will see them no more.’
Kāyassa bhedā na naṃ dakkhanti devamanussā’ti.
This too is how those gods know whether a person has anything left over or not.
Evampi kho, mārisa moggallāna, tesaṃ devānaṃ ñāṇaṃ hoti: ‘saupādisese vā saupādisesoti, anupādisese vā anupādiseso’ti
Here, it appears "saupādisesā" refers to the five aggregates or the "collection" or "group" ("kaya") that is visible and knowable.