My question is about the (un)worthiness of chips from the "deadest" dry hand-friable wood. It occurs to me that perhaps wood in such state is cellulose that is devoid of the stuff that composting microbes want; and further decomposition would have to result from the proximate environmental conditions, and/or be performed by larger critters. Requesting inputs from the knowledgeable.

Ideal as mulch...
Spread over the top of the garden inches deep, will be turned into top soil within months here in the south... And as mulch will prevent seed germination of unwanted plants while keeping moisture present for existing garden.

Dug into the soil? big mistake...

Added to compost? depends on the amount of "green" material you are using...

I can imagine a possibility of a pile of vegetable material from the store dumpster... Decomposing without the added carbon would be a smelly mess. Add the sawdust and the smell is absorbed.

Even cellulose when added to the soil is a worthwhile ingredient for the purpose of soil conditioning. It is organic material and will help improve soil structure and moisture retention. I think studies have shown that cellulose when added to fertilizer mixes can be an even more valuable addition for nutrient accessibility.

If the chips are that crumbly, I would spread them around the garden soon, before there's nothing left.