"The bullet is a fool, the bayonet is your friend"
General Suvorov in the Suzdal Regulations, 1765
Tula was the major arms making center... in fact Tula is where it's located. It's real name is "The Armory of Peter the Great" and right up to 1917 the commanding officer wore epaulets with the cypher of Peter I on them rather than the current Emperor. I'm not certain when the Sestroretsk Armory was founded but I'm reasonably certain it wasn't anywhere near the beginning of the 18th century and may have been as late as the 19th century. As to the patterns, the only reference works I have are in Russian (which I can't read) but I'll take a look and see if I can puzzle something out. Also, the illustrations are terrible drawings, so they don't give us much, if any, detail.
I believe the flintlock military musket was introduced in Russia by Peter I and that the initial supplies of them were purchased in the Netherlands by Peter during the Great Embassy. This would have just about the time the socket bayonet appeared on the scene, the very end of the 17th century but, as we all know, Peter was vitally interested in the latest and best military technology and it's inconceivable he wouldn't have known about it or wanted it. There was hardly a shred of the traditional in Peter and none at all when it came to building a modern military.
Russian flintlocks of all types are very rarely seen. I had one, probably a Marine musket, made at Tula in 1841 that was in otherwise new condition – so much so that it almost looked like a reproduction. It was brass mounted and, aside from the markings, looked like a French musket. I suspect it was a "bring back" from the Crimean War. I was once offered a Russian Brunswick Rifle that was clearly a Crimean War souvenir because it had a long inscription engraved on the patch box saying how it had been captured in the Baltic by the British naval expedition. A few guns associated with the Russian American Company have also surfaced... a bit horse pistol with the cypher of Alexander I turned up in a California junk shop a few years ago and collector Mike Carrick once showed me a musket (similar to the one I had) covered with Pacific Northwest Indian decorations.
Can you tell Russian military history is one of my hobbies?