No, imo.

It doesn't look formal to you because you have no drapes, no art, and a bunch of life happening in there.

My choice would be to do something interesting with paint (the ceiling or the chimney, maybe) and then add finishing touches. Did the chandelier come with the house? If not, there's a wonderful opportunity to make a statement, right there...

No from me. It just chops up the room.

Yes, yes, yes ^^^^ to both above comments.

Your lines are too clean and modern for that kind of detail. Embrace what you have and amplify that. Don't mish mash and go in a different direction.

I agree with what's been said. The bump-out for the fireplace is just going to make any wainscoting look weird, and the wainscoting would make the fireplace look weird. It's possible to be modern (or transitional) and formal; you don't have to pull in traditional elements and muddy it up.