EDIBLE_COOKED is possible, but I think EDIBLE_RAW is more interesting choice as tradeoff: dwarves will be able to seek out raw food not in roast and fulfill their needs, thus increasing focus, but they'll get sick as a downside. Or they may safely eat it after boiling, if they're so lucky to get it. (irl prep note: while frying is kind of cooking, using that will leave them poisonous)
Similar tradeoff could be obtained with something like
giant funnel, which is antibiotic to the point of helping fight off tuberculosis, but isn't exactly favourite thing to eat (and of course, boiling would destroy the antibiotics).
Wet is fine for wet trees like willow, but mushroom tree-specific restriction can only be done with dfhack: i.e. when a mushroom sprouts or is picked near a tree, change its type to appropriate mushroom type if necessary - second one is both easier and guarantees that the poisonous mushrooms won't be avoided by just not designating them with getplants.
(Could also use it to place them wholesale, which is even more complicated, but could do
fungus circles, which may even kill off young spruces with nutrient starving. )
You could also monitor food intake by setting up special smashing/incinerating stockpiles/minecarts for poisonous mushrooms, if looking what you pick isn't enough. Though there's the danger of someone eating it before it is stored in minecart.
There's many others (though not all) in Lactarius family that are edible and non-poisonous after stint of boiling. Russula family also has some that need to be boiled, such as
emetica. I don't really have good knowledge anymore, though - when shops have plenty of food now there's less reason to go into forests and I have forgotten over 90% of what I've ever learned :v