I sometimes use it as a layer on the bottom of nest box, then cover with a layer of straw. Straw keeps the saw dust from getting stirred up too much and the sawdust insulates well and absorbs any broken eggs or other messes.
I am a Very seasoned Woodworker/furniture maker. You want to stay away from woods with a lot of acids in it. Look up wood toxicity levels of different species. Stay away from walnut, oak, wenge, bubinga, zebra wood and Iroko and oily stuff like teak or some mahoganies like Santos. The best shavings I found are the best for bedding is stuff from a molder of shaper(router table). Carvings, lathe shavings minus the fine dust is ok But be careful of the long stuff, It may create injury. You could use the sanding dust and maybe fire pit ash and some sand in a kiddie pool for a dust bath. But yes use the saw dust for the compost, Especially when you nitrate (stanky too wet material) level is up. If it is too dry add lawn mowing clippings to it. Never put animal fats in compost, keeps away mice and aromas. (if you didn't know already.lol)
Oh and go to Local Millwork shops or cabinet shops, Offer to clean out the dust vacs or ask them to bag it for you, Then just make sure to pic it up before garbage day. Trust me I can even get rid of the amount I have.