How can I decorate this empty wall (picture)?

Hang some art and call it a day. Not every square inch of floor space needs to be crammed with furniture. If you feel it is still too lonely, add a plant stand with a low light plant or faux greenery.

I would do a couple larger plants against the wall. Like a fiddle leaf or something like that. Because they are tall, they will help full in the space an add some color!

I have seen some big clocks on hgtv in some very nice homes. Not only does it fill the space with decor but it provides a purpose at the same time. I got one (it was actually a kit) at amazon.com and they have a variety or styles and even different types of numbers. They also carry a huge line of wall decals and by that I don't mean stickers. They have beautiful patterns and themes to enchance any decor. Here is one of butterflys. The butterflies are all separate so you can arrange them anyway you choose. in my bathroom and the one in the laundry room (it is just words).

consider hanging a macrame plant holder from the beam. Use a fake plant

A sofa table behind the couch might look good or a tall floor plant against the wall

Large house plants would look nice there or maybe a gallery wall.

I would center a bookcase under the beam. Tall pants, (real or fake) on each side of the bookcase. Hanging anything on the wall would still look empty.

I would leave it empty just like it is but will maybe consider moving a bit TV towards dining room buffet

I do not think anything on the wall would look good. It would clash with the dinning room. So if you decide on a bookcase don't center it. Put it closer to the living room and paint it white. Same with a tall plant. Don't center it. Put it in one room or the other. Maybe both, tall white bookcases on each side of the TV and a tall plant in the dining room.

What about stenciling the wall something like this pic. c87c12b92f68d9ff53e2f7ea2a3fbb6c.jpg

A stenciled wall will tie the living room to the dining room and fill the wall.

If you are looking to "place something" in the open area, I like the folks who suggested big plants and agree that two work. If you are looking to fill the wall space, I suggest large wall art.

https://www.hometalk.com/diy/decorate/walls/how-to-turn-a-shower-curtain-into-wall-art-37986116

https://www.hometalk.com/diy/build/furniture/how-to-make-a-folding-wall-art-table-with-kyle-schuneman-36124056

use one of those tables maybe that attach to the wall with some bar stools.(some narrow tables don't even attach to the wall-Nice ones at Ashley )maybe move your tv over to corner more ??? or if you can even move your table lengthwise in other direction if you add small table.(i like your floors)

good luck

A shelving unit and a large floor plant.