There's nothing you can do to patch the channels that will make them disappear, and, in fact, a patch will just draw attention to this issue. Whenever I have a problem where I am not satisfied with the appearance or have made a mistake, I try to figure out adding something that will look like an intentional design element. Without you providing a picture, it's hard to make a suggestion, but my first thought would be to use wood trim and either fit it into the channel or use a piece that's slightly wider to cover the channel. I would stain it or even paint it before installing it.

I would build a shallow box cover to fit over the entire area. It would appear to be an architectural detail to the wall itself. You could add another one, any size, on another wall to carry the design. Then paint or stain the same color of the wall. Build it large enough for a mirror to hang from the extended cover.