This will ultimately come down to how you interpret the phrase "each is like a bag of holding," from the description of Heward's handy haversack. If you think that that means the haversack inherits all properties from the bag of holding, except as described, then it's pretty clear what happens when you overfill the haversack. This is a reasonable interpretation, and in some ways the simplest.
If, however, you think (as I personally do) that the above line is simply defining the haversack as an extradimensional space, likening it to a bag of holding simply because that came earlier in the chapter, then it's worth taking a look at other extradimensional spaces in 3.5 and seeing if there's any precedent.
Unfortunately, each extradimensional space is different. Take the quiver of Ehlonna, for example. The quiver is limited by number of items and their type, not any sort of spatial requirements; it can hold eighteen javelins, but not a single rapier, even though that would almost certainly take up less space than the javelins. Or take the spell rope trick, which can hold exactly eight creatures, but size doesn't matter. It can fit eight titans but not nine halflings. When the rope trick ends, it just dumps the creatures out, rather than scattering them to be forever lost like a bag of holding. Rope trick also features the cryptic line
Note: It is hazardous to create an extradimensional space within an existing extradimensional space or to take an extradimensional space into an existing one.
It doesn't elaborate. The only "hazardous" interaction in the rules is between a portable hole and a bag of holding (and, notably, there's nothing in bag of holding's description that prevents you from putting one bag inside another).
So, if it's not like a bag of holding, and it doesn't say explicitly what happens when it's overfull or breaks, how does a handy haversack work? Well, it's limited by volume and weight (it's actually worded as volume or weight, but that's a different argument), and pointiness doesn't matter. So if you fill the main portion of the haversack with exactly eight cubic feet of material, what happens when you try to stuff something else in?
Exactly the same thing that would happen if you were trying to stuff something into a normal space. If it's full of bolts of silk and you're trying to cram a sword in there, you'll ruin the silk. If you're trying to jam a glass jar into a haversack full of rocks, you'll probably break the jar. If you're trying to put a sword into a haversack full of swords, you run the risk of damaging the haversack, which has a hardness of 2 and 5 hit point per inch of thickness. D&D 3.5 doesn't have rules for splitting a bag at the seams, so some amount of DM discretion is necessary here, but it's worth noting that magical items still function just fine until they're destroyed. A suit of leather armor has 10 HP, so a leather haversack probably has a total of somewhere between 5 – 8 HP.
If the handy haversack were to be destroyed, the contents would neither be scattered across the cosmos nor deposited back on the material plane. They'd simply be in their extradimensional space, and you'd need to find a way to access it without the haversack. That's surprisingly tricky, short of sending a very tiny person there via plane shift or having already cast Drawmij's instant summons on the objects you want to retrieve. As discussed in this excellent answer, nondimensional/extradimensional spaces are demiplanes, which are difficult to access as per Manual of the Planes, Chapter Eight. Basically, you'll need to be at the location where the haversack broke to access it, regardless of what magic you use. High level options like crafting a cubic gate or just casting the spell gate will probably do it, or esoteric options like getting a 9th level planeshifter to swap a portion of the material plane with your broken haversack's demiplane. Basically, retrieving the contents of a broken haversack is a high level task, but the contents aren't completely lost.
If that sounds like a headache, it would be quite reasonable to rule that most extradimensional spaces from items dump their contents at the location of the item if it's destroyed, but that would be a house rule; RAW nothing happens, which means they're just stuck in an extradimensional space, and there's no easy way to retrieve them.
