I cannot update World Destroyer, either. I can update the design, but not build it.
If you want to build or upgrade your own World Destroyers, you need to have the technology that grants the Super Laser component. I don't recall what it's called off the top of my head, and it's not something you can easily add using the editor, either; your best shot at acquiring it is to fully research the entire tech tree and then start decommissioning World Destroyers and Devastation Moons at your shipyards. If you're lucky, you'll pick up the tech.
Once you have the tech for it, you can add Super Lasers to any design you want. Super Lasers allow any ship so equipped to blow up a planet, and the tech providing them increases your ship size cap to 4500 or so, which is sufficient to build ships the size of the World Destroyer and Devastation Moon, both of which are around 3000 size (which, incidentally, is a large part of why you cannot really do anything to your current World Destroyers - they're roughly twice as large as the largest standard military ship you can build under normal circumstances; only resupply ships and construction ships can be designed on a similar scale with standard end-game technology).
I tried to S/L to retire World Destroyer many times, not able to get super laser.
When you retire a ship at a shipyard to try to extract technology from it, you have a shot at any technology which went into the ship's design and some which are at similar tech levels to the stuff that went into the design. This basically means that retiring a World Destroyer gives you a shot at getting a tech bonus to any tech in the game, because it's got a tech level 8+ weapon system - the Super Laser. If you want to have a decent shot at picking up the Super Laser technology, then you'll need to have researched most, or preferably all, the standard techs in the game, and you may need to have multiple World Destroyers or Devastation Moons to retire because you're not guaranteed to unlock the full technology with just one ship retired.
But I remembered I wasn't the first to repair the ship.
This does not matter, as long as you're the one that controls the ship.
And some AI had super laser tech in very early game, and I used agents to steal that tech, but when agents finished their missions, no super laser tech found, I've checked the obsoleted tech. This is very very strange.
Super Laser technology most likely requires you to send many agent missions in order to successfully steal it, if a computer player happens to have it. Even if you acquire it, you will not be able to see it (or Super Beam Weapons or Super Area Weapons, the other superweapon technologies) in the tech tree, and you'll need to search in the design screen for a component named 'Super Laser' (or Death Ray for Super Beam Weapons or something like Devastator Pulse for Super Area Weapons).
Sending just one or two agent missions to take any of the superweapon technologies will most likely not do anything more for you than advance you a few percent of the way through the tech's development, assuming that the agent missions are successful. If you have an absolutely spectacular early agent, then maybe you'll get ten or so percent of the way through the tech with a successful mission. It's only when a tech disappears from the list of technologies you can steal from a faction that you've stolen enough information on that technology to be able to reproduce it, and if the faction in question is the only one in the game to have that tech and the faction gets destroyed before you can manage this, well, there went your shot at getting that tech. If you have tech trading enabled, you may be able to buy the tech, but be advised that superweapon techs are even more horrendously expensive than standard techs are.