1st: to add to the ambiance of the storms and maybe certain story locations, something like the psi voices from stalker
2nd: At the highest storm power there could be a blowout at the end of the storm that can kill any unsheltered player or domesticated animal, and at the end of the blowout it either sets the storm strength to a predetermined power level or a random level
Edit: The Idea is for it is to happen at the end of the highest power level storm, giving plenty of time to find shelter in a building or cave. As of the animals it's to force the players to at least build a barn for livestock and not keep them in the open. Also, you can add to this where domesticated animals will seek out shelter at night and/or during storms, so you don't need to drag them into it. Maybe add assignable animal mats/spots that animals seek out when inside. it can even balance it by having no/low enemy spawns, to bring out the "oh no, somethings coming" in the players.
3rd: to add a bit of extra danger to late game storms, I'm thinking something like the trench birds from scp-106's pocket dimension from SCP containment breach. when the player is outside of cover and in line of sight of the birds, the player slowly takes damage. also, optionally the damage can be unmitigated by armor.
Edit: The idea for this is also for it to rarely happen in the late game and but easily countered with a roof or even a tree over your head to be unaffected by it. Basically, a less intensive version of the blowout where all you need is cover. Also, the idea for the health drain, is on its own its slow, weak and won't even kill you, but if you are staying out of cover fighting without recovering it's a problem. Also, it would function more like Dave, where you can see it in distance not being a problem or right above you, being a problem.
I might add more to this if I get more ideas.