Purple wall sucks the life out of the room. Paint the wall the same color as the other walls. Your art will look so much better and the room will be light and bright.

Do you really want to feature that wall? The purple seems to make the room look choppy. Your room will be brighter, cohesive and more inviting if you paint all walls in the same lighter, neutral color.

I would absolutely run it all the way down that way it looks more like an architectural feature. You can brick the wall and maybe do a shiplap treatment to the soffit or just paint it white. I would also put some recessed lights into it... you can get low profile lights - one over each window and 2 just above each corner of the painting. It will give it more purpose. I would look into it to see how big it really needs to be - sometimes these things are built way too big.

You could also carry it around the room to give a tray ceiling effect

Here is an idea of what I'm thinking for brick. I would have to paint away the beige because they won't look right together. We have a small dividing wall in the kitchen that I was thinking to cover with the exposed brick too. Not sure if it would be too much, or if it would tie it together.

If you look at your inspiration picture they have a soffit in there too! It just happens to be going the other direction....I like the brick!

I love the photo of it wrapped around, I'm just not sure how it would work in my space. It's open concept so there is no fourth wall to complete the ceiling in the room. Plus the wall on the left and right of the feature wall are much different lengths. The other issue is that the bulkhead goes down the wall on the right too. There is no way to match that on the left because of the window with beige curtains being so close to the corner. It feels like such a hard space to make pretty!

Something to consider with brick: You will need to vacuum the brick to remove the dust. Are you prepared to do that weekly depending on your location?

Don't highlight a wall with architectural issues! Just paint all the walls (and ideally the ceiling) the same color to make the bulkhead disappear as much as possible...

We have exposed brick. It is a haven for spiders and dust. I would not add where it isn't already. The bulkhead should be painted to blend into the ceiling.

Have you confirmed why its there? Or if it can be made smaller? Thats where I would start

If thete's nothing in it remove it.

If it's hiding something within then just extend it all the way down that wall only.

Having it partially ending looks odd & causes a unwanted focus of why is that there

Color blocking can be a bold way to deal with your bulkhead. Get a color specialist in to help you choose complimentary colors that suit your esthetic.