From High Guard 2e, "Frigate: A small but powerful warship, the role of a frigate is to roam space away from a fleet, patrolling borders and attacking commerce.", "Destroyer: Similar to frigates, a destroyer’s main role is in acting as picket defence for a fleet, eliminating small ships and fighters before they can threaten larger ships.". The Gazelle sounds more like a frigate in both size and mission.
T5 also expands on terms we're using, "Close. Operates closely with other ships (typically the same Space Range). Escort. For defense missions.".
I'm reviewing Third Imperium: Sector Fleets which lists every sector, subsector and colonial fleet for the 12 Spinward Marches subsectors and what ships are in each grouping. I see fleet escorts, escort destroyers and close escorts but no class names. That suggests this particular designation is a placeholder filled by a specific ship type. In peacetime and at the start of war, the best or at least the most available will fill the slot and that means for the sector and subsector fleets the best available escorts. As the war goes on and assets are lost, the next most available units replace them. The Gazelle would serve mostly in colonial fleet and maybe subsector as part of support or escort groups or escort flotillas but not front line BatRons or CruRons UNLESS those are suffering losses and need anything until replacements can arrive. So the Gazelle can have it's place in wartime yet suffer when things don't go well.