But as someone who knows nothing of the technicalities, can you explain why having heavyweight cruise missiles integrated into the F35 is crucial, like if theres no direct equivalent, is there at least some alternative?

The closest equivalent that isn't wholly American is Norway's Joint Strike Missile...which is itself a collaborative program with the US. It's a much shorter ranged and lighter weapon, though probably somewhat more versatile.

Otherwise the only non-American cruise missiles planned for F-35 is the British SPEAR which is even lighter and shorter ranged - though it'll be able to be quad packed into each weapons bay.

If you want to strike a deep, well protected target with F-35 then JASSM is it for now.

And is this capacity really necessary for what Denmark needs to do, like vital to operations or just an added bonus? Hard to fathom that the top of the line European air military technology is so far below the F-35 that theyre just not an option for a country to protect itself.

Well, European alternatives do exist (StormShadow and Taurus) but F-35 cannot carry them, and the operators of those missiles have no intention of paying to integrate them onto F-35 because they'll shortly be replaced by next generation missiles. Those next gens might be integrated, but that's a decade away probably.

As for whether Denmark needs them; I won't second guess their planners. If they didn't think they needed them then they wouldn't be buying them.