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According to James R. Gibson's "Feeding the Russian Fur Trade", supply ships from Okhotsk visited Petropavlovsk in this period annually around October.
Several round-the-world voyages (Nadezhda, Kamchatka) and foreign trading vessels (Lark, Sylph) also arrived.
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Petropavlovk had a harbor, and certainly had its own ships/boats. For these ships, as well as the ships from nearby harbors, the question probably makes no sense. Of the ships from more remote places, there existed the Russian-American company, (see Wikipedia) whose ships probably visited Petropavslovsk regularly. Communication with proper Russia was not by ships but by land.