We really do not know how far back the Soyuz-class starship's design lineage could be traced. It looks like a Miranda-class derivative, but who knows? And how far back would the Miranda's design lineage go? 2265? 2245? Why not 2200 or even the earliest days of the Federation? Canon seems to at least vaguely suggest that there were multiple classes of Federation starships in service throughout the history of the Federation, supposedly suggesting an evolution of design and also a broad mix of designs to carry out various functions needed.
We don't really know what the Soyuz-class starships' official function was, how/why they were built, or what the history was of the class and its lineage. We can only speculate on some very scant facts. Just about everything we know (visual effects aside) about the Bozeman / Soyuz was taken from the discussion on the Enterprise-D's bridge following the Bozeman's hailing:
WORF: Captain, we are being hailed by the other vessel. The computer identifies it as the USS Bozeman, a Federation starship... Soyuz class!
LAFORGE: Soyuz class?! They haven't been in service in over eighty years!
PICARD: Open a channel...
BATESON (on viewscreen, speaking from the bridge of the Starship Bozeman): This is Captain Morgan Bateson of the Federation Starship Bozeman. Can we render assistance?
PICARD: I'm Captain Jean-Luc Picard of the Federation Starship Enterprise. We were just going to ask you the same thing.
BATESON (on viewscreen): Captain Picard, your vessel is not familiar to us...
PICARD: Captain, have you any idea what has just happened?
BATESON (on viewscreen): Our sensors detected a temporal distortion... Then your ship appeared... We nearly hit you...
PICARD: The Enterprise has been caught in temporal causality loop, and I suspect that something similar may have happened to you.
BATESON (on viewscreen): You must be mistaken. We left starbase only three weeks ago.
PICARD: Captain, do you know what year this is?
BATESON (on viewscreen): Of course, I do. It's twenty-two seventy-eight.
PICARD: Perhaps you should beam aboard our ship. There's something we need to discuss.
As this episode had supposedly taken place in 2368, we can readily assume the Bozeman was displaced 90 years into her future. We can also assume that since the Soyuz-class of starships "haven't been in service in over eighty years", the useful (for Starfleet) lifespan of Bozeman and her sisterships ended about ten years after she disappeared from her native time.
It has been pointed out (non-canon) that the people in the studio who came up with the Bozeman's design wanted the unusual spire-like projections to be sensors or some similar instrumentation. There are multiple phaser banks visible on the surface of Bozeman's hull, but no clearly visible photon torpedo launchers. While this does not clearly preclude the possibility that Soyuz-class vessels could have a strong military design, it is interesting to note that if the Bozeman needed the famous "roll bar" armament of the Reliant/Saratoga, she easily could have had it. Instead, Okudagrams seem to assign importance to the aft projections that were said to be sensor or sensor-like equipment. This suggests a much stronger scientific/intelligence emphasis.
The Soyuz-class was already in service when Captain Bateson left his starbase just weeks before the Bozeman's encounter with the time warp. We know this class was in Federation use for about another ten years. We can logically assume that other starship-classes (perhaps the Constellation-class, the Excelsior-class or possible
derivative-classes of these ships) replaced the Soyuz in the performance of her (presumably) science/intelligence duties.
Since it has been shown that ships like Kirk's Enterprise were in service for at least 35 years prior to the Bozeman's time warp displacement, and that the Federation made the practice of upgrading and refitting older ships to newer standards, and that the Enterprise-A soldiered on clear into the 2290s, it can be assumed that Soyuz, or her design lineage, if any, could easily go back in time to at least the 2260s. (Fans have
supposed this in their
artwork.)
If we assume that, for sake of argument, the Federation had long-term goals involving the deployment of starships for special command scientific and/or special command intelligence mission profiles, and that it had been practice for at least a couple of decades (perhaps longer) that said profile was typically assigned to a limited-production modified Miranda-type frigate design, one could call this ship a "command science heavy frigate" or a "command intelligence heavy frigate".