Well, the very traditional wainscotting is a little jarring next to the (better than average) midcentury rustic stone wall. But it's not at all offensive and seems at home with your neutral decor, so I think I'd let it be.

Thank you, appreciate the comment!

I think the stone is lovely and natural. It would be a shame to cover it with drywall in my opinion. You could update the look by painting wall and wainscoting the same colour.

Makes no sense, really, with the wainscoting. Design elements don't live in isolation. Drywall!!! and let it go. Not hard, fur it out, add a solid surface of tile surround, It is "jarring", belongs in a different setting. No reason to let it dominate, and not a "shame" whatsoever, for a more cohesive message in your space. You surmised as much I would guess, or you probably would not ask : ) You were on the right path with the question.

Add a cocktail table and where is tv , if there shall be tv...going?

Rug could be larger too. ...and coffee table ? Yes, please.