IMO fake beams always look fake and in a space with 8' ceilings they make the ceiling feel too low. If you wanted to do something to add interest to the space and warmth add some warm color to the space IMO the shelcves would be a lot more interesting if the back wall was painted a color , adding a rug with some texture and color too would do a lot to warm up the space . In fact I would paint the back of the shelves and the bump out for the FP the same color and before that get a rug that is more interesting and colorful choose a color from the rug for that wall color . Many ways to add warmth without doing the ceiling. If you post a pic of the whole room you will get more help too.

It would be best to consult a local interior designer that can take a look at your house as a whole, find out your decorating goals, and advise with a solution that integrates well with the rest of the house.

You have styled your mantel and shelves very nicely, but that wall is still blah since it's all white, so I agree with Patricia about changing it instead of doing something to the ceiling. It's a lot easier to change a paint color than it is to change a ceiling. That would be expensive and you might get tired of it and wish it weren't there after a while - in addition to the fact that your inspiration picture has a vaulted ceiling and you don't. It won't look the same if you do this treatment on your ceiling.

Examples of using flooring on ceilings here…

https://designingidea.com/tongue-and-groove-ceiling-flooring-walls/

Armstong makes a planked ceiling system. Don't add another major wood tone to this room.

I like the appearance of your room. If I wanted a planked ceiling, I'd select white shiplap to match.

You could do something like these reclaimed wood beams

once you get in your furniture, plants, lighting, it should be fine

I love this one w/the addtion of wood and leather

if you like more of a coastal look, you could do this:

I used Calif Classics (mediterranean) on my master bath ceiling. (click on my name to see all of the pics)

I found 230sq ft on craigslist that someone was selling for a song. My husband and I used construc adhesive and finishing nails to install it on the ceiling.

Around the sky light I got a raw piece of white oak and stained it myself to match the floor color and trim out the edges

if you wanted to do the same w/beams, do a lighter faux beam and wrap it w/a white oak veneer. stain to match the wood planks

If you want to add warmth, the first thing to do is replace the area rug. That one is a big cold sink in the middle of the room.

that's actually a good idea.

here. I photoshopped what charles mentioned. (I also gave you matte black stone surround)

bring in some leather furniture, some greenery, and you're done. I think this looks great

you could also switch out the white shelves for walnut,

photoshopped the walnut shelves w/black sconces on your pic.

I also used the beams from this pic

White oak shelves, black shiplap above the fireplace

perhaps some sort of tile for the surround

Wow thanks Beth for your impressive photo edits. It helps visualize the space