The general wording must, by necessity, be read in light of the qualified report!

It would appear that he wrote the above from memory without checking Nayl, for there he actually says:

‘Ibn Ḥibbān also related it and added: “and when he stood for the prescribed prayer.” Al-Shāfiʿī likewise transmitted it, restricting it to the prescribed prayer, as did others, whereas Muslim restricted it to the night prayer…’—and so on, exactly as we have just quoted from him.

In short, everyone cited apart from Muslim restricts the ḥadīth to the obligatory prayer; hence Muslim’s version, too, should be understood as referring to the obligatory prayer, not to the night prayer as al-Shawkānī claimed. If the supplication is legislated for the obligatory prayer, then it is even more appropriate in voluntary prayers, as anyone of sound judgment will recognize.

There is also a narration in Abū ʿAwānah and in Ibn Khuzaymah’s Ṣaḥīḥ, no. 462—likewise in Abū Dāwūd and others—with the wording: ‘and I am the first of the Muslims.’

That clause appears in most chains of the ḥadīth, as I noted in my commentary on Ṣifat al-Ṣalāh, p. 84, and its strength is further corroborated by another ḥadīth cited there.

I draw attention to this because I found Aḥmad Shākir, in his notes on the ḥadīth in al-Rawḍah, saying that the phrase is unattested, which requires clarification. Accordingly, there is no objection for the worshipper to say in his opening supplication, ‘and I am the first of the Muslims’—not as a statement about himself, but in emulation of the Prophet—peace and blessings be upon him—who in turn was following his father Abraham—peace be upon him. It may also simply express one’s haste to comply with the divine command, as I explained there; see that discussion or consult Zad al-Maʿad.