Not sure what you mean by freshening up. Cleaning it? Or covering it in some way? Hard to tell the colour - is it gray or brown?

You'll get the best help if you post photos of all 4 walls of the room. Is that your own furniture or the previous owner's? Is the gray carpet staying?

Find someone that can do a diluted muriatic acid wash of the wall. It takes some protective equipment so I wouldn't try it yourself.

Some rock walls can be tweaked to be attractive. Yours is not one of them Too many things going on with the wood fire insert, the vents and the mantle mounted too high.

I would strip the rock off and start from scratch.

It’s grey with moss and lichen on it. That is not my furniture. The carpet is blue and will be replaced one we close on our current home. The room only has 3 walls. The moss rock wall, the dark paneling wall, and a plain white wall with big windows.

Should I paint it? I’m not sure how to lower the mantel. It’s grouted into the wall.

Paint cannot fix this unless it's invisible paint.

IMO you want to end up with something like this.