Hi. I could be wrong, but with several wall angles all in white -- wondering if a rug medium neutral would anchor the space [more than a white rug].

Neatened border in simple neutral goes with alot.
Aniline leather retains the hide's natural surface [not the uniform surface of a topcoat paint or insoluble pigmented sealant.]

Safavieh Natural Fiber Nf443A Solid Color Rug, Maize/Wheat, 10'0" X 14'0" · More Info

Aniline Leather Lounge Chair and Ottoman, White, Ash · More Info

Does this repeat the angles a bit? could be nice, and with solid upholstery. Repeats greys of fp and appliances, a small mention.

My Texas House by Orian Agave Natural Area Rug, Gray, 9'x13' · More Info

White or black table & chairs

Congratulations! Looks like a lovely house! What do you think about throwing in some soft blues with your white and tan/caramel palette?

Is the bookshelf space supposed to be the dining room?

Hello! I'm a home stager and to prevent the room from looking over crowded, you can put the lounge chair next to where the bookcase is. If not, a simple rectangular bench will do: https://amzn.to/2Rk3uhM

Place a few throw pillows on top of the bench and sit them upwards (and lean them against the wall at an angle) to add some elegance: https://amzn.to/32oWAhz

Over by the bookcase, a faux fiddle leaf tree by Nearly Natural will be nice and their quality and shipping is great: https://amzn.to/2FzyxU9

Where the books are, I recommend canvas art or a large mirror in that space. I would remove those books because they look misplaced.

The white and tan combination would be beautiful and the comment above about adding a rug with blue hues (preferably navy blue) would compliment the space very well. This one is a great price because 8 by 10 rugs are usually very expensive: https://amzn.to/33m8mZr

At Home has some fantastic area rugs as well and they don't cost too much.

It will look beautiful afterwards! #affiliatelink

What's the purpose of that bookshelf area? Form follows function. Do you want a game or play area for the kids? Or a reading nook. I have a reading nook in the living room. Comfy chair, art on the walls along with bookshelves and display of an heirloom doll collection (you may collect something different, just using it as an example, or even just nice dishes or vases or whatever you need shelf space for besides books), table and lighting. I have almost no indoor good light sources so in my reading area, I have plants on the table that is against the window. Only spot in the house I can enjoy a houseplant, YMMV.

But if it's meant to house a table and eating area, then that's another way to go, and the shelving area would be for dining items . . . maybe some baskets, etc. If you have crafty kids, it might be an arts and crafts area . . . etc. We need more information on your living area needs . . .