Seems that it's probably a fossil coral, the outer layer etched off by bog acids.

The axe looks wonderful indeed! How did such stone axes work though, is stone not too brittle? I assume it was sharper when used too, right?

Ever seen an axe for splitting wood? Doesn't need to be that sharp... Just needs to be wedge shaped with decent heft behind it and a long handle. This particular axe could be a tool, or a weapon used more like a war hammer (those were a thing). Metal war axes typically had shorter handles, less weight but a sharper edge.