I’ve got a few areas on my car that have etched clearcoat. I’ve gone over it with chemical guys C4 with a medium cut, heavy cut, and microfiber pads. The result is below. Should I move on to wet sanding or try a different compound?

From the looks of that picture, and it may just be the picture, it appears it is in the primer, under the base and clear.

Being your car, you know if this just popped up. Can you feel it with a fingernail? If not, then it may be time for a light 1500 sanding and cut/compound/polish.

Yeah, you are not going to remove that with a cutting compound. 1500 grit if you've wet sanded clearcoat before, or 2000 grit if you havent with a DA orbital.

Move to 3k foam pads and then your compounds.

If you havent already, wash it down with an iron remover and get as much surface contaminants off the clear coat as possible before you sand to keep from grinding it into the new surface.