Cabochon inlay

I’d like to carve a design into the face of a cab, let’s say black onyx, and fill it with crushed cultured opal. I’ve done this on metal but never on a stone.
Once I get to the grinding off the excess opal step, what comes next? I have no experience in lapidary, but maybe there’s a way to polish up the face of the cab once the opal inlay is ground down flush? I have a flex shaft and/or a small polishing machine to work with. Any help is appreciated!

Since your crushed material (which would be resin bound, I assume) is
going to substantially softer than the base material; if it was me, I
would bring the carved base material to the final sanding stage, then
level the filler out before working out to the polish stage. It might
even be easier to do all but the last couple of polishing steps before
setting your fill.

thank you!