Well, we use our strength mainly in combat, our intelligence mainly in crafting, and our dexterity mainly in avoiding danger. Our senses, however, we use all the time. Our general situational awareness and ability to make sense of what’s going on is ALWAYS important, and should probably have effects on anything and everything. That said, actually applying it that way would make it boring as hell, since you could never have low perception and maxing it would have little or no tangible effect.
As for more things it would make sense for it to strongly affect, ranged combat is the first thing that comes to mind. I heard an idea, probably on Discord, of using it to modify headshots. I.E low perception makes it nearly impossible to get headshots, higher perception gives you a better chance. I rather like it, effectively making it the crit chance stat for ranged, while dex is the crit chance stat for melee.
There’s also something to be said for overmap ranges, since that can make a big difference ingame, actually knowing when there’s a useful location nearby or just driving past because you can’t see it can make a huge difference.
I like the idea of it modifying hearing quality, but that’s currently handled in a nearly binary fashion, I.E you have good, normal, or bad hearing. Trying to expand that might get difficult.
Having it modify the chance at which you can identify items/enemies isn’t a bad idea. Something along the lines of anything beyond triple your perception tiles away is just listed as “small item” “item” or “pile of items”. Enemies too, could be “humanoid” “small quadruped”, etc. High perception would help keep you safe, while taking low perception makes you roll the dice on how close you’re willing to let a potentially dangerous creature get before you know if you can fight it, possibly with the ability to activate binoculars or a rifle scope to get a better look at something far away.
Once stealth mechanics get fleshed out it could be exceptionally useful, letting you spot hidden enemies faster and from a longer distance, but also letting you use your senses to determine whether your own hiding spot is adequate, helping you sneak more quietly and stay out of lines of sight, etc. While most of that would be primarily player input, there’s something to be said for noticing a stray stick or piece of gravel before you step on it, or noticing that your foot is sticking out of the long grass you’re hidden in.