I'd think about re-arranging the room so the TV stand is where the bar currently is. And yes, I'd add both recessed lighting and perhaps one large chandelier centered on the fireplace. Paint all the trim and the wall color; remove the wallpaper. Pick colors that will work better with your gray upholstered furniture.

If the ceilings aren't more than 8 feet high, I would not coffer it. Looks like there are can lights in the recess/bar area. Do more of those, but don't neglect table and floor lamps, as well as accent lights (art lamps and uplights) to give the room an intimate, cozy feeling.

I would not add anything to the ceiling that will make it feel lower.
I personally would remove the texture and do some more detailed crown molding. (See images below and how the moldings are kind of on the ceiling...)

You can also do a shiplap kind of thing. But I personally like shiplap on walls or a vaulted ceiling.

Sabrina thanks, yes we were going to wall up the bar to extend a closet beside it then planned to move the TV to that wall. decoenthusiate ceiling is 10-1/2 feet.