How do we reconcile the verses about not oppressing orphans and treating them kindly, with the Prophet's supplication against an orphan girl, which broke her spirit until she cried, knowing that its chain of narration is authentic?

A Muslim must be respectful when speaking about the Prophet (peace be upon him), for he was merciful even to animals, as evidenced in the hadith (definition) of the camel that complained to the Prophet (peace be upon him), and the hadith of the bird (hummarah) that was distressed over its chicks.

As for what is mentioned in the hadith of the orphan girl, to whom the Prophet (peace be upon him) said: "May you not grow old," it was a gesture of affection and jest. The Arabs used to employ such phrases without intending them as actual prayers, similar to "May your right hand be covered in dust" and "May your mother lose you."

The Prophet's (peace be upon him) statement that any prayer he makes against his nation, for which they are not deserving, Allah will make it a purification, a blessing, and a means of drawing closer to Him, was meant to comfort Umm Sulaim and reassure her, not because he was angry with the orphan girl. This hadith is evidence of his excellent character (peace be upon him) and his kind treatment of children and orphans, as stated in the Almighty's words: ﴿وَإِنَّكَ لَعَلَى خُلُقٍ عَظِيمٍ﴾ (And indeed, you are of a great moral character).