Oliver Cowdery initially wrote “to dust” in 𝓟; then without any change in the ink flow, he supralinearly inserted the (giving “to the dust”). This change appears to be an almost immediate correction to the reading of the original manuscript, no longer extant here.
Elsewhere the original Book of Mormon text consistently has the definite article the in the phrase “to (the) dust”:
In fact, 35 out of the 36 occurrences of dust in the Book of Mormon text are preceded by the; the only exception is found in a biblical quote: “and their blossom shall go up as dust” (2 Nephi 15:24, citing Isaiah 5:24). The critical text will therefore accept the corrected reading “in the dust” for Mosiah 21:13.
Summary: Maintain in Mosiah 21:13 the corrected reading in 𝓟: “and they did humble themselves even to the dust”.