When copying from 𝓞 into 𝓟, Oliver Cowdery initially wrote “after his holy order”, then somewhat later inserted “the manner of ” supralinearly, probably when he proofed 𝓟 against 𝓞. (The level of ink flow for the first two words is slightly heavier, which suggests that he redipped his quill before correcting the text.)
Elsewhere, the text has examples of only the shorter “after God’s holy order”:
Of course, the expression “after the manner of X” occurs frequently in the text (32 times), but there is only one case where this expression and “God’s holy order” are combined to give “after the manner of God’s holy order”—namely, here in 2 Nephi 6:2. Clearly, there would have been no motivation for Oliver Cowdery to have edited the text here by adding “the manner of ”; thus the original manuscript undoubtedly read “after the manner of his holy order”.
Summary: Maintain the expanded phraseology “after the manner of his holy order” in 2 Nephi 6:2; Oliver Cowdery’s corrected reading in 𝓟 was undoubtedly the reading of 𝓞.