Not sure should I build this.
Good instinct.
For a battleship this has a quite sad amount of firepower - frankly, I have a hard time believing this is 40,000 tons given what is actually on it, and while the jump drive is probably limiting you I can't believe it's the entire problem as this ship has less firepower than I'd expect from a ship half the size (even from an NPR honestly).
You have 5x2 15-cm lasers and four each of AMM and ASM launchers. In a recent campaign my 20,000-ton cruisers could still mount 4x3 15-cm lasers and six ASM launchers (size 6, so a wash matched against your sizes 1 + 5). At the same time, you're pulling 4000 km/s out of ion engines, which is okay for a missile cruiser but a beam ship needs to be much faster - my aforementioned cruisers pulled 4500 km/s with ion drives and this was a mediocre compromise to meet the tonnage limit (it was an RP design, else I would have had more engines and less weapons).
So you have a 40,000-ton ship that can be outperformed by a 20,000-ton ship fairly easily, and in exchange you get...what? Jump capability, for sure, yes. A few more layers of armor, also. But no command modules, pretty poor maint life, a rather short deployment time that makes it difficult to use this for anything besides sailing from point A to point B, shooting things, and sailing back - for example, this thing will be a pretty poor JP picket which is a lot of firepower to not be available to you in that case.
Aside from the jump drive, it seems to me that maybe this ship is leaking tonnage in different directions without a clear design focus: you have chunks of tonnage going into sensors, troop capacity, cryo modules, etc. that is probably excessive. Additionally, the missile loadout is frankly just useless - 4 ASMs contributes almost nothing to a salvo (unless you're planning to mass these? Really?), and 4 AMMs might hit one incoming ASM out of a salvo. Presumably if you have a 40,000-ton shipyard you have enough other yards to build specialist ships with the jump drives, big sensors, troops, missiles, cryo rescue berthing, etc. and you should delegate those capabilities to those ships and make this thing a lean, mean alien-killing machine.
Pick lasers or missiles as the primary weapon. If lasers, you don't need 10,000 km/s tracking turrets for a weapon designed to kill other large warships - honestly, even if you're using them against fighters or FACs, dropping to 5000 km/s will give you a 50% hit rate and you can mount more guns for your main mission, no reason to go overboard here. In this case missiles are secondary or not at all - use reduced size launchers and magazine space for just a few salvos so you can use missiles to run down fleeing ships before they outrun you - or to kill the fighters/FACs we mentioned. If missiles are primary, use smaller lasers (10 cm) in point defense configurations - ideally get capacitor tech so they can fire every 5 seconds. In either case, your secondary weapons are
secondary - you have other ships to be your escorts, missile boats, sensor pickets, and so on, so use them.
I'd recommend dropping the jump drive and using either a specialized variant or a smaller cruiser-size ship to tote the jump drive around for you - this will also help with maintenance life. For a battleship, more dakka is the correct answer...and also more vroom. Get at least 5000 km/s, with a 160% boost frankly you could be pushing 6000 km/s but keep fuel efficiency in mind here and maybe consider a less-boosted engine.
