How many HP does an item have? (eg, a silver headband, a scabbard, a wood box...) I think this is an obscure theme in the rules, but still quite important.
It's largely a judgement call on your part. You need to come up with roughly how things are built and extrapolate using the Additional Rules chapter.
There's is an HP per inch of thickness guideline in the Damaging Objects section of the rules. And most special materials have it listed wherever they are listed.
But, you have to sort of extrapolate from there.
So a leather scabbard is, maybe, 2 inches thick. So it would have 10 HP.
A wood box depends. A thin crate (inch thick) would have 10 HP. A thick, sturdy chest might be 2-3 inches thick, so 20-30 HP.
And so on.
There are clear rules on both Hardness and Hit Points of objects based on substance.
There is an entire section of the rules dedicated to damaging objects, in fact.
The only real "judgment" would be in how to determine the Hardness/HP of that Silver Headband mentioned - Silver and Gold are both softer than Steel and Iron in real life, and and Gold is shown to have a Hardness of 5 in the rules, as opposed to 10 which is Steel, meaning Gold is roughly about as hard as Wood in game terms. Silver should probably also be 5-6 Hardness.
OP was about HP, not hardness. That takes determining how thick and how much of the materials there are. That's a huge judgement call as without it you can't determine HP. So, judgement call.
Thanks for your help :)
However (judgment call, anyway)... A giant smashes a tower (as seen in several illustrations, for instance), is it a Break DC (if so, which is the Break DC for a tower?) or a hit against AC and damage?
Smash with a club? AC and damage. Break DCs are for sheer force of strength. Think bending an iron bar with just your hands. If them using a weapon is hard to believe, remember an illustration could be an exaggeration, does not communicate how many times it's been hit before, if there's some structural flaw or general shoddy craftsmanship, etc.