Cardboard, and all the chemicals it is processed with
does break down. That's what fungi are for. And if you have a healthy garden, the fungi are busy de-toxifying all of the things that you mention. Even fungicides. See, you can't really kill fungi, you can just inhibit their growth. That's what makes fungal infections so difficult for medical personnel to treat. You get enough fungi ganging up on some "fungicide" and they
will get the upper hand and decompose it.
Here's a page from the
North American Mycological Association showing all the interesting paper products, like toilet paper and cardboard, that can be used as substrates to grow mushrooms. And if you are a little leery of eating oyster mushrooms grown on chemically treated cardboard, don't be. Fungi digest their food before they ingest it, so unlike fish that just pass DDT up the food chain unaltered, fungi will break down the DDT first, then incorporate it into their growing tissue.