Is he who slept before the 'Asr Adhan while tired and woke up an hour after the 'Asr Adhan and prayed considered to have delayed the prayer or to have slept through it, given that he took all measures to wake up before Maghrib?

Sleeping before the prayer time begins is permissible, even if it is highly probable that the prayer time will be missed, because the prayer is not obligatory at that point. Therefore, your sleep half an hour before Asr carries no sin, and it is not considered delaying the prayer. It should be noted that some scholars hold the view that one must take measures to wake up, such as setting an alarm, otherwise sin would be incurred.