I don’t remember Han using stun shots in the movies. Also, if a Stormtrooper is stunned, why would they react to the pain?

But you don’t need to speculate

If I’m speculating it’s because I enjoy this conversation, not because it may help OP as the movies never specifically said “yup, this trooper is dead from this shot fired with Han’s blaster”.

If you want to take things to extreme, you could say maybe no one onboard the destroyed Star Destroyers from RotJ died, you could say Yoda was literally 800 when he met Luke (hello EU), you could say Lando is a very, very advanced droid, you could say maybe Threepio has lightsaber-related subroutines in his CPU. Nothing in the movies says the opposite, which is why you don’t see “Lando’s a human” in OP’s fact list.

I’m repeating myself here, but OP’s asking for facts, for undeniable statements, and “Stormtroopers die if they’re hit by a blast shot” is not an OT fact, or at least I don’t remember any of the movies giving full confirmation. It’s implied or suggested, but OP’s free to choose a different way for the RPG game OP’s designing.

And I simply believe that “Stormtrooper armor can save you from potentially lethal shots but you can get KO’d” is a better theory than “Stormtroopers wear useless armor just because”. Even if you take the mostly non-serious nature of SW77 in mind.