So the point must be clarified. I say:
This ḥadith does not support that claim in the slightest, because the phrase “between every two adhans” actually means “between an adhan and an iqamah.” Al-Ḥāfiẓ said, “The commentators have treated this as an instance of taghlib, like calling the sun and the moon together ‘the two moons.’ It is also possible that the iqamah was termed an adhan because it too is a proclamation—only it announces the imminent performance of the prayer, just as the adhan announces the entry of its time.”
I add: whichever explanation one prefers, the second “adhan” in the report is, by unanimous agreement, the iqamah; therefore the proof cannot be stretched to support the position just mentioned.
Furthermore, even if we were to take the ḥadith at its literal, widest sense and include within it the adhan added by ʿUthmān—despite the fact that such an adhan unquestionably did not exist in the Prophet’s lifetime—the most it would establish is the desirability of an unspecified, unrestricted voluntary prayer. Yet that is not our question. The issue is whether this prayer is a confirmed, regular sunnah, and whether it consists of exactly four rakʿahs. For that, no reliable evidence exists—neither this ḥadith nor any other—as has already been demonstrated in detail.