Okay, we'll leave the themes subject alone for now. However, I don't agree that I'm missing the depth because the themes don't resonate with me. I'm deeply interested in human themes; it's probably the main reason I read fiction. I'm also a fan of children's fiction and fantasy. But the utter poverty of new ideas and/or new directions in the HP books inevitably leads to the predictability of the characters. For me, anyway.
I'm glad to hear Dudley finally develops a bit beyond flat-pack bully. But, really, he was another missed opportunity. I did in fact read the first chapter of I think the 5th book where JKR tells us Dudley has taken up boxing. Great, I thought, a chance to show how the discipline and self-restraint required to box will change Dudley; he might even become an ally for Harry. But no, she has him use his boxing skills to be an even better bully. I stopped reading.
Moving back to the principal question in the original post which concerned the method of dealing with backstory in trilogies or series of a greater number.
In the literary fiction area, two examples came to mind in response. I read the second part of John Updike's Rabbit series (two of which won the Pullitzer prize) without having read the first. He made absolutely no concession to the backstory. Part two was complete in itself and at no stage did I feel that I had lost anything through not having read its predecessor.
Similarly, in Evelyn Waugh's Sword of Honour trilogy, surely his most significant work, managing to entertain superbly while dealing with profound issues and discarding the flippancy which affects much of his writing, each part stands totally on its own feet. Each simply plunges straight in.
If you think about it, backstory has to be there in any novel for it to make sense. So there should be no reason why, in a sequel, it should be any more obtrusive than it would have been in a novel without a prequel. The sequel needs to take into account what went on in its prequel but does not need to repeat it.
To look at it in an odd way, if you had already written a novel about characters in their forties and then later decided to write a second about the same characters in their twenties, you wouldn't agonise about your first novel not having explained what went on in the second one set earlier. You would just make sure that the second didn't contradict the first.
But I can see that, in the more commercial arena or some sectors of it, a different approach might be needed. Horses for courses.
Chris