Contrived...
as I said, contrived.
Having read POD, Fifth Frontier War, Fleets of the Fifth Frontier War etc, this is what the Trojan Reach SECTOR Fleet looks like (I think):
2 x "Uashki" Second Line Battleships
1 x "Planet" Heavy Cruiser
3 x "Atlantic" Heavy Cruisers
1 x "Azhanti High Lightning" Strike Cruiser (in this case acting as a Strike Cruiser)
2 x "Gionetti" Light Cruisers
2 x "Skimkish" Light Carriers
1 x "Ritchey" Fleet Escort
1 x "P F Sloan" Fleet Escort
7 x Destroyers (Something worse than the "Midu Agasham")
5 x "Chrysanthemum" Destroyer Escorts
3 x "Fer de Lance" Destroyer Escorts
8 x "Gazelle" Close Escorts
Now we also know that the Tobia Colonial Fleet, at minimum, can provide 4 Patrol Corvettes and 1 "Ulfhednar" Escort Carrier! Several other Imperial planets in the Reach may be able to muster similar Colonial forces, Pax Rulin for example.
You can add in the sub-sector fleets of Pax Rulin, Gazulin), & Tobia, which probably consist of 1-2 Destroyer Escorts and 3-6 Close Escorts or Patrol Corvettes each. Pax Rulin & Tobia may also have an old destroyer as part of their sub-sector fleets. The Realgar naval base in Sindal may or may not be a base for a Sindal sub-sector fleet, if so, likely very small!
As to why the Imperium does not stomp all over pirate bases in the Reach after Treasure Ship, well "Game of Sun & Shadow" is that answer to the loss of the Treasure Ship! However that adventure also provides a very good answer why the Imperium has to be very careful, stomping around the Reach:
"As Captain Lenat pointed out, one of the reasons that
past punitive flotillas have just swept through the Reach
and returned home was to avoid the impression of a
military build-up on the border with the notoriously
touchy Aslan." (POD page 170)
Now The Glorious Empire sourcebook makes very clear that that the Hierate does not build Battleships, only the Glorious Empire has done, the "Syokhtai" class. However one "Syokhtai" wouldn't last long, one on one, against a competently handled "Uashki" Second Line Battleship. Also however, the Glorious Empire fleet, despite their battleships, still lost the Battle of Hliye, against the far far more numerous 'smaller' ships of the Ya’soisthea Aslan. The Imperial Navy is thoroughly outnumbered in the Reach, and cannot afford to even hint at breaching the Peace of Ftaheir!