Now it looks like serpentine. Much like that found on beaches near Gold Beach and Brookings, Oregon. Green quartz is still possible, but the cleaned stone looks more to serpentine. Jade is still unlikely, in my opinion. Still, cutting quality serpentine (can not determine this by photo alone) is still a good find.
Time for more coffee.
Edit: Blew up the images and noticed the white stringers. That is quartz. The stringers are quite common in serpentine found in costal areas of southern Oregon and Northern California. I am now convinced you have serpentine. Cutting quality? A good lapidary with experience with this type of stone will tell you. It looks good, but images do not
tell all.