It's mostly carbon, yes....
It's the whole circumference of the seat post that you apply the paste to, (but obviously at the level where it sits just out of sight). Some of the paste does need to contact that wedge.
On the picture below I've marked my saddle height (at the red line), then raised my saddle, and I'd then apply the assembly paste at the yellow area, all the way around the post, before dropping it to the correct level and tightening the bolt.
It'll feel gritty / sandy as you push the saddle down.
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