Stoning married adulterers is a revelation from Allah ﷻ. This is why the Prophet ﷺ and his companions did so. The verses you quoted on flogging refer to unmarried adulterers.
In the khutba of a Friday prayer, 'Umar ibn Al-Khattab responded to your question:
حَدَّثَنِي أَبُو الطَّاهِرِ، وَحَرْمَلَةُ بْنُ يَحْيَى، قَالاَ حَدَّثَنَا ابْنُ وَهْبٍ، ...
There are at least four cases of Muslims being stoned to death according to the Hadd of Zina (adultery) in the time of the Prophet, as recorded in the major Hadith collections.
Maiz ibn Malik of the tribe of Aslam:
A man from the tribe of Aslam came to the Prophet (ﷺ) and confessed
that he had committed an illegal sexual intercourse. The Prophet (ﷺ)
In the Qur'an, there is a concept called zina (زنا), which refers to both fornication and adultery.
In the early days of Islam, the punishment for zina was confinement to the house or corporal punishment. The woman would be confined to the house until she died or another piece of legislation came into force. The man would receive corporal punishment.
Stoning does not appear in the Qur'an (ref.). It's instead mentioned in multiple hadith, e.g.:
The Jews brought a man and a woman who had committed illegal sexual intercourse, to the Prophet and the Prophet ordered them to be stoned to death, and they were stoned to death near the mosque where the biers used to be placed.
Sahih al-Bukhari 7332
Does illegitimate oral sex of a married man or a woman require a Hadd
punishment such as Rajm?
Zina which carries Hadd is only intercourse in which penis enters vagina or anus. Not for sex between the thighs, hands or mouth etc. because these are not called farj. Consult https://islam.stackexchange.com/a/818 and https://islam.stackexchange.com/a/40018
Its a ritual. I'd rather not get into the discussion of why rituals are carried out ... The Hajj enacts actions of Prophet Abraham and his wife Hagar. Specifically the stoning ritual is about the Sacrifice of Prophet Ishmael.
Prophet Abraham had a dream in which Allah commanded him to sacrifice his young son (Ishmael) in His name as a test of his devotion. ...
First of all trying to find a logic or scientific explanation to religion is not always good. Science is a progressive information. New evidences can prove old theory or rule may not be correct.Still, If you need a reasonable explanation to stoning of Satan, this may help:
Actions influence attitudes
cognitive dissonance: changing attitudes to ...
All perfect praise be to Allah
You should read rajm-wikipedia page, their is some information in fiqh section. Also it must be kept in mind that rajm/stoning was not a new kind of punishment, it was an old punishment which was also practiced by Jews of that time(it was present in their scriptures too), so there was nothing new to explain. Though we ...