in basic mechanics, there's no obvious problems. However in general i'd say your ships are underarmed. The Butcher's one medium laser and 10 short ranged missiles isn't much to kill things with; the Wagner's 60 AMMs won't make much of a difference to incoming missile salvos - though you take what you can get against box launches.
I'd suggest cutting into the fuel bunkers to increase armaments. I'd also suggest finding room to fit ECM on beam combatants. You may also consider rebuilding your engine tech to eliminate the thermal reduction. It's massively increasing the costs of your ships, and making it impossible for your destroyers to repair their engines in the field.
I would also look into creating a long range missile combatant. With your evident tech it should be fairly straightforward to create a billion+ kilometer standoff attack missile.
As TDS says, there doesn't seem to be any mechanical problems with the ships; they'll work just fine. So all I can really suggest is changes I'd make to the design to fit my preferred fleet strategy.
As far as optimization, well, I usually try to specialize my smaller ships. To give an example, on a ~8000 ton destroyer, beam and missile fire controls are significant chunks of total tonnage, so I usually go for either one or the other. This is less important on larger ships like your cruisers, which have the tonnage to fill multiple roles effectively. But you've used the opposite design strategy I do, with multi-purpose destroyers and specializing cruisers.
The missiles are, as noted, slow and fairly short ranged, though with a powerful looking warhead. You might be able to get away with this since you're using box launchers; they're easy to shoot down but they'll all be coming as one massive wave. Without knowing the weight distribution it's hard to suggest optimizations, though, and they'll probably work fine if you have enough to overwhelm enemy PD.
For the Butcher specifically, the beam fire control can't match the tracking speed of the ship, so I'd suggest swapping it out for a 12,000km/s fire control, even though it will be pretty hefty. This will make your spinal laser more accurate against fast ships, and let any smaller lasers you add operate as effective point defense weapons. Lastly, I'd take the thermal sensor off; the Hunter has a much better one, anyways. Maybe replace it with a size 1 active sensor just so the Butcher can still target its lasers if the Hunter gets taken out. The range is long, but that's a matter of preference as much as anything.
The Hunter could use more armor. It's considerably more fragile than the Butcher, despite the fact that its enormous active sensor will likely make it a priority target. You might want to offload the resolution 1 sensor onto the Wagner; that would give you more space for armor and I prefer to have multiple anti-missile sensors just in case one gets taken out, anyways. It also doesn't have enough MSP to repair its largest component, probably the engine, which means it risks a catastrophic maintenance failure that could leave it crippled or potentially even destroy the ship if the engine explodes.
The Wagner's lasers don't really need to be on turrets; the ship already moves at 12,000km/s, so they're only gaining 33% tracking speed from the turret. I'd suggest taking them off, switching to a fire control with 12,000km/s tracking speed, and replacing them with more numerous hull mounted weapons; lasers if you're dedicated to them, or potentially small caliber railguns (with their multiple shots) if you want a short range PD weapon. AMMs might benefit from launch tubes instead of box launchers, especially considering you only have one fire control; generally you aren't going to want to launch all 60 missiles at one target, so it wont fire them all at once anyways. Might do better to put 5-6 missile launchers with a 5 second rate of fire and some magazines. Like the Hunter, it needs more MSP to repair the largest component.
Like with the Wagner, I'd replace the Devastator's turreted lasers with hull mounted ones, and CIWS with railguns, to take advantage of the ship's high base tracking. That or work on a higher tracking speed turret and fire control, since the difference between 12,000 and 16,000 just isn't that big. Since it's a dedicated beam escort ship, it doesn't really need the resolution 100 sensor; it can use the anti-missile sensor just fine for targeting warships at anything like beam range. It also could use better armor; in my experience bigger ships, and ships with active sensors, tend to be priority targets, and the Devastator is both.
The Legacy is actually probably closest to a ship I'd design. The combination of spinal laser, secondary lasers, and railguns gives it a good variety of beam weapons, and should probably be capable in both anti-ship and anti-missile roles. I'd probably take the CIWS off, since as with the other ships it doesn't track much faster than hull mounted weapons, and give it a small size 1 active sensor just so it has a backup for painting targets if it loses its escorts. Other than that, it's a solid beam combatant.
