Kamchatka today has cultural projects like universities and museums, but in the early Russian period it was considered a pretty desolate place. Among other deficiencies, there was very little for the few literate residents to read. They could acquire manuscripts, and priests or monks could have had printed Bibles, but early on, getting a book would have been tough. Wintering ships with their own libraries most likely sailed away with them. Excluding Bibles, what was the first printed material owned and kept in Kamchatka?
My assumption about ships' libraries may have been in error. Chamisso, in "A voyage around the world...", wrote about his trip on the Rurik, on which in 1816 he found in Petropavlovsk not just books, but several volumes useful for his expedition. According to Chamisso, these books had been accumulating in Kamchatka "since the time of Bering" (early 1740s). Governor Rikord let him take with him several of them, on the condition that he return them to the Academy of Sciences, which he claims to have done.
I have no reason to doubt this report so I consider it the best answer available at present.