The Shulchan Aruch's organization is based on that of the Tur. In particular, here, the laws listed in the question are presented in the same order, with the same section-numbering, in the Tur. So, the question is why :22 and :23 are in that order in the Tur.
When the Tur presents the laws in 61:16-22, it does so without explicitly citing sources, presumably indicating that either these laws were not matters of controversy to earlier authorities or that the author felt comfortable implicitly choosing sides if there were any such controversies. However, in 61:23, the Tur cites the laws about sheva and dagesh in the name of the Rambam, and then quotes the Raavad as objecting specifically to the Rambam's rule against pronouncing a sheva nach as a sheva na. (The Shulchan Aruch, in mentioning the Rambam's opinion but not the Raavad's implicitly decides in favor of the former, consistent with its author's explicit disagreement with the Raavad, expressed in his Beit Yosef commentary on Tur 61:23.)
So, perhaps the Tur presented this particular law after all of the others about pronunciation because its details weren't universally accepted by previous authorities. I'm not sure if such late-ordering of more-controversial rules is standard in the Tur, but I'll note that the remaining two sections in that chapter, :24 and :25, both also contain citation notes, in that the former is cited in the name of Rabeinu Yona, and the latter includes a "And there are those whose practice is ..." note.
