Was it obligatory for someone who slept through Fajr prayer until sunrise to set an alarm or similar device, taking into consideration that the Messenger of Allah (peace be upon him) slept through Fajr prayer during one of his campaigns until sunrise and did not order anyone to wake him?

The questioner's statement that the Messenger of Allah, peace and blessings be upon him, did not order anyone to appoint someone to wake him for prayer is incorrect. Muslim and others narrated that the Messenger of Allah, peace and blessings be upon him, ordered Bilal to watch over them (guard them and wake them for prayer) during one of the غزوات (expeditions).

This hadith is evidence for the permissibility of using an alarm, especially for those who know they will not wake up at prayer time, for the means to an obligation is itself obligatory.