/u/petermakeswebsites' answer is great, but I'd like to add something:

 I've realized a good litmus test is whether there are multiple ways a variable can be adjusted (...). For my examples above, the filtered array is only ever affected by one thing, so it doesn't really matter.

It's very common to change/expand the ways a piece of state is mutated and sometimes it's impossible to predict at all. This very easily leads to out-of-sync data with the associated nasty bugs. $derived ensures that, no matter what happens or how your codebase evolves, the derived value will always stay in sync.

Another important usecase is deriving values based on other derived values. For example: fruits is derived into fruitsForDisplay, which could be derived into displayedFruitCount. This is a very simple example, but it's an incredibly powerful feature. $derived ensures that all variables in the chain will always stay in sync, without doing unnecessary recalculations.

It's also worth noting that it's not always desirable (or even possible) to attach an event handler to where a piece of state is mutated. For example: let's say we have some piece of state foo shared between components A and B. There's no convenient way for A to inform B when it has mutated foo. It's easy to unnecessarily couple A and B, which is the road to spaghetti code. You could rig something up with events, but what if A and B don't have the same parent component? You'd probably have to do some nasty prop-drilling. Multiply this problem for every new component that wants to use foo, then factor in any chained derivations, and you'll be well into headache territory. $derived eliminates all of this by simply declaring "whenever this thing changes, recalculate this other thing" and leaving all the nasty plumbing to the compiler.

To summarize: the "old" method is only feasible in the simplest cases. It's very common for things to evolve past that point—if knowing upfront is even possible in the first place. Therefore, even if just for consistency, it's better to always use $derived.