Is the Hadith of the gecko authentic? Can its authenticity be questioned? And to what extent does it impact our understanding of the issues of animal free will and inherited sin?

The reason for the command to kill geckos is derived from what is mentioned in Sahih Al-Bukhari and Muslim, where the Prophet, peace and blessings be upon him, called it a "fuwaysiq" (a small transgressor) because it is among the harmful creatures, and it deviated from the nature of most insects by increasing harm and injury. Among the reasons for commanding its killing is that it used to blow fire on Ibrahim, peace be upon him, when he was thrown into it. It was also said that it is a devil due to its rebelliousness and distance from goodness, and that it is one of the harmful venomous creatures. In summary, the command to kill geckos is because they are harmful and injurious, and in addition to that, their kind is malicious, corrupt, and devilish.