I agree that they’re back for two reasons, money and royal adjacency.
They’ve shown time and time again that they have no intelligence and no strategy.
I suspect they are running out of money - rich beyond the wildest dreams of most people but not rich enough to sustain the lifestyle they want, and Harry made the assumption that coming back here would revert their security provision to what it was before they left.
Probably someone at some point said something to him like “you’re not resident here hence the bespoke arrangement on a case by case basis” and being a bear of very little brain he assumed without asking that by moving back to the UK it would just default back to the provision it was before, not considering that their status is entirely different now.
He’s also desperate to get back into the royal fold given that he has nothing else to offer and their money making efforts are failing badly, and he’s desperate for his kids to be seen as royal, which has a better chance if they’re brought up in the British schooling system and develop English accents.
I honestly don’t think either of them will have stopped to think about any of it more than that, hence they’re flailing around furiously now that their plan, such as it was, hasn’t worked.
As an aside on the whole “paparazzi near the school” thing, even if they haven’t made it up, it’s such a non event. I mean nothing actually happened, no photographs were taken, nobody invaded the school ground - and even if photos had been taken it’s photos, not a threat to life. I’m not saying it’s fine for children’s privacy to be invaded, but this is not the kind of thing that requires armed taxpayer funded security.
I live very close to Lambrook school and drive past it periodically, and it’s always completely quiet like any other school. It didn’t even twig to me that it’s where the Wales’ kids go to school until recently. And that’s a known and publicised place.