“the mu’adhdhin says it while delivering the adhān,” which is problematic.)

I say: That additional wording explicitly states when the supplication is to be made—before the adhān is finished. The apparent meaning of the ḥadīth is that this alone exempts one from repeating each phrase after the mu’adhdhin, especially according to those who hold that such repetition is not obligatory, which is the view of the majority. In that case there is no need to harmonize the two reports, and the difficulty vanishes. Allah knows best the true reality.

This understanding is confirmed and reinforced by the wording of the ḥadīth of ʿAbd Allāh ibn Masʿūd, traced back to the Prophet: “No Muslim says, when he hears the call to prayer—the caller proclaims ‘Allāhu akbar,’ so he proclaims ‘Allāhu akbar,’ then the caller testifies that there is no god but Allah and that Muhammad is the Messenger of Allah, so he testifies to that, then he says, ‘O Allah, grant Muhammad al-wasīlah…’” The ḥadīth continues, and its chain is sound, as will be mentioned, God willing.

It is also permissible at times to confine oneself to saying, “Wa anā, wa anā” (“And so do I, and so do I”) instead of repeating after the mu’adhdhin, “I bear witness that there is no god but Allah; I bear witness that Muhammad is the Messenger of Allah.” This is exactly what the Messenger of Allah ﷺ used to do.

The report comes from ʿĀʾishah, may Allah be pleased with her: when the Messenger of Allah ﷺ heard the mu’adhdhin pronounce the testimony of faith, he would say, “Wa anā, wa anā.” Abū Dāwūd and al-Ḥākim recorded it through the route of Hishām ibn ʿUrwah, from his father, from her. Al-Ḥākim said, “Its isnād is ṣaḥīḥ,” and al-Dhahabī agreed. I add: it also satisfies Muslim’s criteria, for Muslim transmitted it through the chain of Sahl ibn ʿUthmān.