Aslam-o-alaikum and may peace and blessing of Allah be upon you
We need critical thinking and knowledge on this subject. Hence I have done my best to provide whatever I know (allahmdullilah) and the sources (scholars which use Quran and Hadith hence these are the most reliable one's).
The misconception is a common one that apostasy results in death because looking at Hadith itself is insufficient and must be backed up with Quranic evidence. This is not a simple case and even scholars differ on this issue. The most compatible analogy is of the scholar Sheikh Suhaib.
Know that there are two broad categories of apostasy: individual apostasy and apostasy with treason, and second is more punishable by death (this is more generalized for your understanding and there are actually three types of apostasy).
The individual apostasy doesn't equal death according to this scholar because the Hadith regarding this is generally worded. Also the Hadith carries only one transmitter and isn't confirmed by a second invidual. Nevertheless it is still classed as Sahih (authentic) but interpretaions are wide.
I agree with Sheikh Suhaib because Quran and Hadith follow in parallel. Quran says "Let there be no compulsion in religion" which agrees most with Sheikh Suhaib's analogy that simple apostasy doesn't carry death. This would against the teaching of Quran (as cited in the verse above) if the case was otherwise.
Also one other point note is that during time of Prophet Muhammad (pbuh) there were jews who conspired against Muslims. They had planned to convert to Islam and then leave to create restlessness and division among the Ummah. So another interpretation along with earlier one is that it might have been said to counter the plan of the Jews and Christians, after all hypocrites are more dangerous.
Another common analogy is given at answering Christianity:
When Prophet Muhammad peace be upon him executed apostates, he did it because Muslims were at war time and because Islam was still partial, and Muslims needed protection from the hypocrites of the Jews and Christians who purposely entered Islam and deserted it later to create confusion among the Muslims.
*Now the point to note is that there are different interpretations and go with one that conforms with the Quran the most. Hence I am in agreement with this analogy. Even (for argument sake and my own analogy) if apostasy=death then Islam wouldn't have spread as it has now since time of Prophet Muhammad (pbuh) because the non-muslims wouldn't convert for they would have viewed Islam as an intolerant deen. But non-muslims enjoyed living under caliphates of Muslims and most of them "reverted" to Islam due to the treatment they received (as under their authority) and there are historical instances of this.
Islam means comes from "peace" hence death for a simple apostasy would defy the spirit of Islam, hence it is to reasoned that there is more to than just an individual apostasy.
Allah guide us, and protect us from hell. Any weaknesses are on my part.