That is definitely a strange-looking wall. Do NOT put up ship lap. It's not appropriate for the architecture of your home.

Do you want to keep the fireplace, or remove it and start with a smooth, flat wall?

No to shiplap. It appears that the wall is covering something, maybe brick? If it were my house, I would love to know what’s behind the wall, but be careful what you wish for, could open a can of worms, lol. If it is covering something, I don’t like how they did it. I would tear it down and redo it so it’s flush with adjacent wall. It could turn out to be more expensive than you want, be prepared for the mystery reveal! And let us know what you find!

Have a contractor open the area above the fireplace up to find out what's behind and go from there. Am not sure why it is furred out.

Definitely weirdness. I’m also prone to think that the brick goes up further than you can currently see. Who builds a fireplace with brick stopping that low?

As for a tv, I’d put it in the corner where the clock and sticks are.

I agree it's probably covering the brick; kind of reminds me of textured wallpaper. I like the way it looks in your space, actually. Agreed that shiplap would be a giant decorating mistake if your house has modern style. TV over fireplace could mean rearranging the room etc, I agree with the suggestion to place it in the corner instead of over your fireplace.

I think I will demo it and just put up fresh drywall. I’m not entirely sure there is brick behind it due to where the brick ends on the far right. I could be wrong. We will see! Just curious what the reason is to put the tv in the corner and not over the fireplace?

Television in the corner instead of over the fireplace is because your neck will get sore having to look up at a television over a fireplace. There are MANY posts on Houzz and internet sites with the exact height measurements for a wall mounted television.