How authentic is the story of the mouse and the lost nation of Bani Israel, and is the mouse drinking sheep's milk but not camel's milk one of its signs?

The aforementioned hadith (definition) is authentic, and it states that a nation from among the Children of Israel went missing, and the Prophet, peace and blessings be upon him, believed they were mice because mice do not drink camel milk, which was forbidden to the Children of Israel, but they drink sheep's milk.

This was an ijtihad (definition) (independent reasoning) by the Prophet, peace and blessings be upon him, before it was revealed to him that Allah does not create offspring for those who are transformed (masukh). Consequently, those who are transformed perish and cease to exist, and monkeys and pigs existed before any transformation occurred.