AFAIK, no Russian boats have torpedo tubes in the configuration that you've described. They all go into the inner hull, usually at the top of the bow, with the exception of the Severodvinsk class, which uses the same torpedo tube configuration as our boats (at least according to the published publicly released diagrams).Might be a defensive turret installed when it became obvious that those small Dominion "battlebug" attack ships didn't yield to standard phasers... A desperation move rather than a well-integrated weapons system.
While not used in American ships (mostly because the USN uses single-hull designs rather than double hull-within-a-hull design), Russians build external torpedo tubes into the outer hull which are not reloadable in combat. In fact, it would be a challenge to reload them outside of port, since you'd have to haul a torpedo out of the hull, then insert it into the external tube, without falling off the front of the ship.
So I'm entirely willing to entertain the idea that the docking bay tubes are either one-shot (or even cluster shot, like a MLRS) external tubes, or some kind of prototype weapon that just happened to be field testing onboard Enterprise that really wasn't a conventional torpedo.
I know of several older designs retrofitted to this configuration; the Typhoon and Akulas, for example, have these small torpedo tubes built into the outer hull that can be loaded with lightweight torpedoes, supposedly for the purpose of quickly launching and intercepting enemy torpedoes (a sort of underwater CIWS). Some Chinese submarines--which are essentially smaller knockoffs of Russian designs--are also designed this way.