What is the ruling on the Fajr prayer that was performed after the adhan of sunrise due to a lapse during ablution after the adhan of Fajr, and what is the expiation for that, knowing that there was no intention to delay it?

It is advisable to strive not to prolong one's stay in the restroom due to its health detriments. And initiating prayer at the beginning of its prescribed time is among the best deeds. If someone misses a prayer due to an excuse, such as sleep or forgetfulness, there is no sin upon them, and they must immediately make up for it. Missed prayers can be made up at any time, even during the forbidden times for prayer, according to the soundest opinions of the jurists. Therefore, you were correct in promptly making up the prayer, and there is no harm in performing the supererogatory prayers before it.