Commercially conventional grown plants are often more watery or how I should describe it, than stuff you grow yourself. It’s because commercial, conventional growers grow stuff fast with artificial fertilizers, to get as many crops/year as possible. (You can see the difference, organic veggies are often smaller and less “perfect” to look at, but when you taste them, their taste is better.)
Maybe that’s why your bunny reacts to store-bought produce. Always rinse very carefully. And introduce slowly, just like you would introduce all new types of veggies. If I give my Bam a bunch of store-bought parsley he’s guaranteed to get sticky poop, so I only feed him a sprig or two/ day. My other bunny happily eats the rest of it, his stomach seems to be of stainless steel. Your bunny may be of the same type as Bam, the extra-sensitive type.
Organic is very expensive here, like 4 times the price of conventional plus I have to go a long way to get it, so my buns most of the time have to make do with conventionally grown greens during the winter. As long as you’ve got really good hay, bunnies will manage.