Can we get some pictures of the ships from the saved linked here? I'm away from my desktop that has Star Sector so I can't check the builds personally (and I'd probably not have the patience to download the specific modset used anyways)
Based off Hiruma Kai's incomplete description of the fleet in question, the builds used spark very little confidence.
To be fair, sometimes you just can't find the weapons you want. Especially in a heavily modded game where weapon pools can be very diluted. Then there's building fleets to do different campaign jobs. The fleet in the save is clearly not focused on combat, but rather campaign speed, stealth and sensors. To be honest, it looks like a reasonable fleet for smuggling or stealth missions. Combined with Navigation and Sensors, the ship has a ridiculously small profile, strong sensors, and a base burn speed of 11. Other player skills are Helmsmanship, Impact Mitigation, Shield Modulation, Missile Specialization, Wolfpack tactics, Energy Weapon mastery, and Field Repairs. The skills themselves are also modded.
Anyway, I present a break down of the ships as requested for those who don't want to download the mods/save.
The Fury has:
0 Caps, 3 Vents
s-modded Dedicated Targeting Core, s-modded Expanded Missile Racks
Insulated Engine Assembly (lowering profile)
Fuel Additive (15 OP for +1 burn, 20% less fuel consumption, but makes engine more unstable, 25% more maintence)
ECCM Package
Pirate Handiworks (0 OP, 20% less profile)
Converted Hangar (Broadsword wing)
1x Ion Beam, 1x Graviton Beam, 1x Kneecapper MRM (dual regenerating energy/emp missile,base 6 ammo), 2 tactical lasers, 2 mining lasers, 2 PD lasers
In the saved file, the Fury has a cautious officer with Helmsmanship and Strike Commander - but as noted by Deshara, officers were shifted around. I think the ship does better with an aggressive officer instead of cautious personally. Reckless would also likely be an improvement. There's a level 5 Reckless officer, level 3 aggressive, and level 1 aggressive as well, plus the player.
The Moray (phase skimmer destroyer) has:
0 Caps, 0 Vents
s-modded Expanded Missile racks, s-moded Fuel additive (see above)
Insulated Engine Assembly, Pirate Handiworks, Expanded Magazines, Converted Hangar (High Tech Talon Interceptor, 7 base OP - 11 in this hangar, 4 fighters, light machine gun, bright missile each), High Resolution Sensors
2 Heavy Burst Lasers (forward mounted), 1 burst laser (rear mounted), 1 Kneecapper MRM (forward mount)
Brawler (TT) had:
0 Caps, 9 Vents
Comes with insulated engine assembly built in
s-modded fuel additive, s-modded high resolution sensors
Pirate handiworks, Stabilized Shields, Resistant Flux Conduits, Hardened Shields, ECCM Package, Armored Weapon Mounts
2 Salamander MRM, 1 Ion Beam, 1 Graviton Beam
Hedone class yacht (Time splitter frigate) had:
0 Caps, 10 vents
Civilian Grade Hull built in
s-modded fuel additive, s-modded militarized subsystems (note burn speed 10 + 2 = 12 with this setup)
Insulated Engine Assembly, Pirate Handiworks, Reinforced Bulkheads, Escort Package, High resolution sensors
2x Light dual machine guns (forward mounted), 1 IR pulse laser (360 degree turret)
Kite (A) had:
1 cap, 1 vent
Civilian Grade Hull, Militarized Subsystems built in
Pirate Handiworks, Expanded Missile Racks, Insulated Engine Assembly, Escort package, ECCM package, Reinforced bulkheads
2x Hammer torpedoes (so with Missile skill, 12 total torpedoes), 1x Prickler PD Turret
Given the 4 additional civilian ships (Buffalo, Valkyrie, Phaeton, Salvage Rig) are also configured for minimum signature, maximum speed (burn 10), and sensors (high resolution sensors), the insulated engine assemblies on the frigates unfortunately aren't doing much, given the largest 5 ships are used to determine sensor profile.
As I noted before, letting the fleet fight, it looks like it is engaging the enemy to me according to officer AI. But given it's a speed/stealth build instead of a more combat focused build, it doesn't fight as well as it might, which can certainly cause problems. The other way to look at it, is the purely AI enemy side (for example the Merchant fleet) has no issue engaging and destroying ships in the fleet.
While I think it's perfectly fine to make suggestions about the tactics the AI might want to consider using (run in with shields down and armor tank), I'm not seeing this unwillingness to engage. Especially if I hand edit all the officers to all reckless.
Certainly in this case, the suggested behavior for the mission brawler would be non-ideal for the beam Brawler, Hedone or Kite, for example.