Another trick would be to get the same style, but paint or wallpaper the backs (if they have backs) in a combination of colors that unite the pieces. So for example, let's say you have a gray sofa and turquoise pillows and a beige rug. You get some wallpaper with those colors in a fun pattern and put on the backs to brighten and unite.this is just one wallpaper, but your get the idea. Notice how the oranges in the room and gray carpeting are brought into the bookcases. Of course, you could always paint them all a single color.

We have an engineered hickory floor throughout our living, dining and office. We used the tile shown here in both the entry area that adjoins them as well as the hearth. I wish I had done the kitchen at the same time The tile has both light gray and light brown in the stone effects, so looks nice with our gray walls but also the varied shades of brown in the wood floor. https://www.artwalktile.com/products/monocibec/ethnos/ethnos-tile-huron-54850. But your kitchen colors, especially the cabinets, would be a big factor in tile color choice! Good luck!

The wood tones look good with crisp white (more on the blue side). Gold/orange likes to sit next to white, either crisp or cream (yellow based). But it does NOT like to sit next to gray. It takes a VERY special designer (ahem...the one that none of us can afford) to get golden wood to work with muddy grays. I would go WHITER with the floors than what you are showing. Your cabinet choice is showing BLUE-gray. That's fine. One of the PRETTIEST floors you can put next to 'wood tones' = blue slate! I kid you not. As you've noticed you can go DARK blue or you can go WHITE-blue. Notice the 'blue' in both? Yep. Cause blue helps 'set up' the gold tones and the gold tones help set up the blue tones. They make each other pop. I would stay away from the gray and stick with white or super dark blue.

I took a look at the photos in your ideabooks and see that your taste is far more modern than your traditional house. You may be trying to make it something it is not through sheer force of will. I urge you to hire a professional designer to help you marry the two styles. Hopefully, one of the pros on this forum will help if hiring a designer is not in your budget. This photo from your ideabook might be a good starting point. Did you save it because you like the floor color? Could you get a sample from a flooring store to see if it clashes with your fireplace stone? It’s difficult to judge colors on monitors, so really needs to be seen in the actual space. The beautiful trim in your house look wonderful painted white. I would hold off on adding a beam until your vision is more complete with the elements you already have.