That link doesn’t have any references in the Qur’an at all to killing apostates. Merely that apostasy is condemned by God and will be punished by Him.
This is unlike the Old Testament which does prescribe the death penalty for apostasy:
“If your very own brother, or your son or daughter, or the wife you love, or your closest friend secretly entices you, saying, “Let us go and worship other gods” (gods that neither you nor your fathers have known, gods of the peoples around you, whether near or far, from one end of the land to the other), do not yield to him or listen to him. Show him no pity. Do not spare him or shield him. You must certainly put him to death. Your hand must be the first in putting him to death, and then the hands of all the people. Stone him to death, because he tried to turn you away from the LORD your God, who brought you out of Egypt, out of the land of slavery. Then all Israel will hear and be afraid, and no one among you will do such an evil thing again.” - Deuteronomy 13:6-11
Regarding the “Hadith” - that is, people claiming that Muhammad said something at some time - they contradict one another, Muslims disagree about which Hadith are correct, and there is good evidence that Muhammad forbid the collecting of Hadith (sayings), claiming that the Qur’an was the correct focus for Muslims.
If one wants to understand apostasy at the time of Muhammad, it is important to realize that the Muslims had been attacked by various tribal groups who were seeking to kill and enslave them. Under those particular conditions apostasy constituted treason (ie: changing sides in a war).
I haven’t seen any evidence that the Qur’an prescribes the death penalty for apostasy.