Get a thin piece of granite cut to size pretty simple or even just a piece of laminate in a plain color cut to fit exactly. None of those plants look very happy there so maybe find some that like the space.

How long have the plants been up there? If they aren't doing well, you could leave the area empty. Often these areas were meant to add drama by being left open.

If plants usually do well, you can have an aluminum tray made to fit the space and finished with a half inch lip to stop drips.

Two of the three plants are not doing well and will be replaced. They are all about 8 years old.

One of the things I'm looking for is if I get a thin piece of granite, how to make the transition between the granite and the wall below the plant ledge.

What is scratching the surface? If it is the pots, you could just add felt pads to the bottoms. Less than $2 at a home center.

Early on I didn't have felt pads on the bottom of the pots. Now I do so there haven't been recent scratches.