> Is there a way, without mining or waiting for treasure drops, to acquire "a <stone> pebble"? Like, can I order a rock from a crafting society and break it into pieces or something?

No, but if you do a carving project using a larger amount of stone than it calls for, the extra piece will be leftover. You can generate a pebble that way.

For example, you can order a large rock and then start making 'a small <stone> block'. Since this calls for a small stone's worth of material, it will create a leftover pebble. You only need to do the first carve, and then you can throw away the partially completed project.