All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The last two ahaadeeth indicate that the effect of the poison remained in the Prophet's system until he, sallallahu ‘alayhi wa sallam, passed away. These ahaadeeth were cited by both Al-Bukhaari and Muslim. They were not cited by Al-Bukhaari alone.
As for the first hadeeth that was cited in Imaam Ahmad's Musnad, Ibn Katheer wrote about it, "It was cited by Imaam Ahmad only in his Musnad, and its chain of narration was hasan (good)..." [Al-Bidaayah wan-Nihaayah] Al-Arnaa’oot classified it as saheeh (sound). This hadeeth clearly indicates that cupping has an effect in extracting poisons from the body.
Ibn Al-Qayyim mentioned this in his book Zaad Al-Ma'aad, clarifying the wisdom behind the fact that the effect of the poison remained in the body of the Prophet, sallallaahu ‘alayhi wa sallam, after the cupping:
"Poisons are treated both by extracting the poison and by using the proper antidote to neutralize their effect. Whoever does not have access to the antidote should use complete extraction, the best method of which is cupping ... When the Prophet, sallallaahu ‘alayhi wa sallam, used cupping, he did it in the upper part of the back, which is the most direct route to the heart, and so the poison was extracted with the blood, in this case only partially. A weak effect of the poison remained in the Prophet's system in order to fulfill what Allah, The Exalted, had decreed for him; to die as a martyr in order to receive all ranks of virtue. When Allah willed for him to die as a martyr, the effect of the poison reappeared so that the decree of Allah would be fulfilled." [Zaad Al-Ma‘aad]
For more information, please refer to fatwa 260611.
Allah knows best.