I don't follow MP so I can't speak to the meta, but I can see some pure optimization problems just from looking at the pngs.
Your ion trees aren't binary. You're adding two individual beams to the last combiner which is terribly inefficient. On the first ship you have four beams combining on the first prism and then add two beams to the main beam on each subsequent combiner. This is terribly inefficient. On the third and fourth ships, you appear to have two individual beams and three pairs going into the penultimate combiner. This is not quite as bad as the first ship, but it's still very inefficient. I also doubt you really need both repeater prisms. You need the last one so the long snout doesn't eat your range and if you opened the armor around it a little bit it would actually be useful, but anything that gets close enough to kill the last repeater is probably in range of the last combiner. Really, though, I'm not sure how much the long snout really adds. The two with the snout are clearly inspired by a BH ship so I've fought ships like that. The snout discourages me from shooting into the ion core, but it would do that at a third the length which would have far less rotational inertia and ships with spinal mounts that lack swivel live or die by their turning speed.
All your crew rooms are red tinted so either you're not using crew roles or you're deliberately obfuscating them with identical uniforms, which seems unlikely. Look up OneEye's crew management guide in the guides section of this forum. You'll be able to move crew out of the way to free up walking space or cram components closer together.
You have a lot of small reactors. I suspect you'd do better with fewer, larger reactors and storages. If you use crew roles you'll save on crew and have clearer or shorter walking paths, which will pay for the storages you need. Ship number two the small reactors are out of the way enough I think they're excusable, but the other ships you can probably make work without most of them. This may be related to your pure redshirt crews if you're managing them with compartmentalization.
You should probably be using engine rooms at the scale you're building at. Maybe not on the first ship, but certainly the second ship the way the engines are clustered together and probably the third and fourth. Ship number two could dro three boost thrusters if it attached the others to a couple engine rooms and save money while improving reverse thrust and maybe other directions if some other engines fit around the engine rooms. Engine rooms power adjacent engines so you probably save crew and since they're room operators you can stick them off in out of the way corners if you use crew roles and assignments.
FTL is either a complete waste or you should have them more central. The first two ships don't have it so I suspect for your purposes it's a complete waste. They're costing you two extra tiles of hauling for the shields that have paths through them in addition to their actual cost.
If I saw these as BH opponents the only one that would worry me is the second. The others I think I could take with a fast ion or missile ship that circles at about 250 meters.
EDIT: A reference to an AI ship handling issue that was fixed in the last update has been removed. The second ship will maneuver just fine.