Don't take this the wrong way, but I don't think you understand Adams. He was incredibly logical. That was his genius: He would extrapolate on every topic to their logical conclusions - from computers to science to religion.
When he was being absurdist, he was very clear about it. Like you said, he was writing about conkers as if it's just the same in the rest of the galaxy, which is definitely absurd. But in order to ground that absurdity, the rest has to be normal. He doesn't just drop in complete nonsense.
So the question remains: What part of British culture or Adams personal history am I missing where it's logical for an adult to happen to have a bunch of chestnuts on hand to give to children?
> "Don't take this the wrong way, but I don't think you understand Adams."
In my opinion (as a Brit who isn't an expert on Douglas Adams, but has read his books) the person you replied to was completely right and it's you with the misunderstanding.
When he was being absurdist, he was very clear about it. Like you said, he was writing about conkers as if it's just the same in the rest of the galaxy, which is definitely absurd. But in order to ground that absurdity, the rest has to be normal. He doesn't just drop in complete nonsense.
So the question remains: What part of British culture or Adams personal history am I missing where it's logical for an adult to happen to have a bunch of chestnuts on hand to give to children?