Great point, I didn't even think about that until you mentioned it. Although the apocalypse was more than 1000 years ago if your claiming it was WWIII or the exodus from Earth or the war between the Federation and the Empire. Now if your talking Thargoids then its been a little over 100-200 years since that ended. You'd think they'd have rebuilt in that time, but then I still fly and Eagle MKIII and that model is over 100 years old too. I think all the ships in the game are technically about 100 years old iirc.
Well the thing is, the economy we see in the game points to it as being a world that never recovered from the blows it got, which by the way were not few with WWIII followed by a thousand years of continous conflict at both big and small scales, think not only of the war itself but the long lasting effects it had, in the economy of the bubble in Elite Dangerous we have huge populations but the economy of the entire system is threatened by a single commander with 500tons worth of domestic appliances.
Remember the people with ships are a minority with huge luck, the world is similar to that of the tv show Dark Matter, for example, there are huge corporations with enough resources to build stations and capships and other stuff, then there's an small amount of indie pilots with ships and then there's the big chunk of population stuck on poor colonies that don't even have electricity because no one can afford it and the corporations screwed them over decades if not hundreds of years before.
Also, as you point out, most of the tech is really old, the only new thing in recent history was the Frame Shift Drive, which has basically made the economy in the whole galaxy go boom, as it has allowed access to a huge ammount of resources previously out of reach and lowered the costs, however, the FSD was only discovered in the 3290s and only got really popular in the following decades, which means only a handful of people actually have one.