In 1813, Petropavlosk became the administrative center of Kamchatka, but it was still tiny. How often did ships stop there around the time of this change? Likely, many of the voyages were to Okhotsk, Kodiak, or Novo-Arkhangelsk.
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.
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.