Bismillah,
Asalamu Alaykom,
The concept of stoning isn't mentioned in the Quran but is mentioned in the ahadith.
Stoning is also found in various passages in bible such as the following:
"20 If, however, the charge is true and no proof of the young woman’s virginity can be found, 21 she shall be brought to the door of her father’s house and there the men of her town shall stone her to death. She has done an outrageous thing in Israel by being promiscuous while still in her father’s house. You must purge the evil from among you."
Deuteronomy 22:13-21
Therefore, no one from the Christians or Jews can try to argue that such a punishment is evil or wrong since they all believe that God legislated it at one point or another.
As for the Islamic view, stoning is among the various Islamic penalties (hudūd) however, such punishments have different conditions in order for them to be implemented. It is not a simple matter for such punishments to be implemented and not any random person can do so.
In the case of stoning, 4 upright and just witnesses must have witnessed the sexual penetration occur at the same time. This is stated in ahadith such as from Imam Ja’far al-Sadiq (as) where he gives the analogy of the act being seen like how a pencil is dipped in a pot of ink.
Now such a condition is very difficult to be achieved and this leads one to believe that such a punishment, is meant to be more of a deterrent and highlight how grave the sin of adultery is.
So adultery if not proven by witnesses, would then be proven by admission of the person or both parties. We find that narrations show that whenever a punishment of stoning was carried out, this would have been done due to multiple admissions by the ones who did it. The philosophy of Islam however encourages one to not expose their sins and that they should instead, sincerely repent.
Some of the ulema would also state that such punishments can only be administered under the government directly led by the ma’soum and that within our current time, these punishments, wouldn’t be able to be carried out due to the absence of ma’soum.
Such punishments are meant to also be a purifier in this world and the punishment of the world, is way lighter than that of the akhira.
May Allah grant you success
