With the current abundance of food in the game I'm surprised short rests are free. Surely like a 10-15 supply cost for a short rest, and forced 2x short rest before long rest unlocks leading to a total of 70 supply cost for a day.

This would solve the "long rest after every minor/major scuffle cheese rest abuse" because you'd burn through your supplies too fast.
Changing the companion camp cutscenes to also trigger after a short rest(where it's not required to be night time) would help to keep the companion story progressing with the lower long rest quantity.
Would actually encourage the use of spells like Prayer of Healing, or even just using the healing spells because you can't just spam rests to heal up or you'll run out of supplies. Currently I haven't used any healing spells because you can just drink the healing potions(that are WAY too frequent to acquire) during combat, and then outside of combat you can just press short rest or long rest.

Would probably also contribute to the game feeling more like a tabletop campaign where you can't just full heal for free after every fight.

And just to cover my ass from people who think that would make the game too hard, just make it a toggle in the settings to have "realistic rests" or something. Maybe even make it so on Normal and higher difficulties rests have costs, and then on easy and story mode they don't.