I am not an expert, but imo, I like the chairs--

The room is a dramatic size, so can take some large, interesting pieces. Let's start with the fireplace, which looms over the room. Before you buy new furniture, hang a substantial raw wood mantel on the fireplace wall to break it up. Place a large, beautiful skyskape over the mantel, which will echo the outside sky visible through the flanking windows. Then pull one of the neutral colors from the painting for your sofas. More streamlined sofas could be in a beige linen, blue pillows, maybe a blue print rug. Do fill your fireplace with a huge armful of birch logs to lighten that side of the room--kind of a sky and earth effect. Make sure the rug is oversized to balance out the height of the room and all that flooring acreage. A very large, wide modern atomic pendant light that gives the effect of a mobile would look amazing in the middle of the room.

I would use the side of the room where you currently have your sofas as the "adult" space, and the corner where you have the play rug as the "kids" space. You need to separate the two. So move the desk to the adult area - either on wall to the right side of the opening to the family room, or slide the sofa under the window closer to the other one and put the desk on the wall between the sofa and entry. Move the two tall storage units to the staircase wall, and use them exclusively for toy and game storage. The kids kitchen can go on the wall to the left of the doorway opening. From your entry, you will see mostly the adult area, and the messier toys and all the shelves won't be immediately visible. One other option that could work depending on your floor plan is combining your living room and dining room in this space, and using the dining room exclusively as a playroom.

Two quick thoughts... One: if you would add dimensions to your sketch it would be helpful. It wasn’t apparent to me where the piano fit on your floor plan. Seeing the photo of your room is helpful, but still doesn’t give accurate information about wall space, doorways, and the size of the window. Two: I don’t play but that looks like a cramped, uncomfortable place for the piano. It seems to me to be the least likely place for listening and playing. If I understand you, you want four really comfortable chairs arranged in a circle around a beautiful cocktail table. I’m sure the pros here can suggest upholstery, a stunning rug, and a table to give you a beautiful space. Just please, please go to a furniture store and sit in any chair you are considering. I will never understand buying chairs, sofas, and mattresses online. Of course we have back issues in our family so I take a long time to purchase these items so we can sit in comfort. I also have a SIL who is a tall and muscular size so I buy dining room chairs for his comfort, not dainty darling chairs for looks. The secret to entertaining is comfort, personally, I would pick the upholstery first because the four chairs will be the big expense, then pick a wonderful rug to anchor your space. The piano needs to be moved to space where some cabinets or shelves can anchor and enhance it. My DD has a beautiful antique jelly cupboard in original blue paint by her baby grand to give height to the space and serve to store her music. In your case, it could also house cocktail napkins, trays, etc for your evening entertaining.