Lovely room, I adore the built In! You have plenty of room for your circular seating area. Some over sized wing chairs would work, check out Arhaus. If you keep them neutral, you can add lumbar pillows in a southwestern print. I'd keep the bench for extra seating if needed, a rustic coffee table would work. Arhaus also has some iron and copper topped tables.

Put the 11 x 16 rug under the dining table. (I also suggest you remove the table runner and replace the candles with all cream colored).

Not sure you will be able to get four chairs and round ottoman spaced as in your inspiration photo, but have you considered a semi-circular sofa, facing fireplace, with a round ottoman?

I like the idea of an animal skin rug , too.

Invest in these fabulous chairs for the fireplace, or switch them out with the host/hostess chairs.

I did consider a semi-circular sofa or even two love seats facing one another. The one below seemed more formal than I was going for. bI really want it comfortable and welcoming for after diner drinks/conversation. Our style is early California/Santa Barbara.

Your home is beautiful. Very spanish and I love the beams so I would try and stick with a spanish style design. Once you get a round coffee table it's going to be a lot easier to visualize the layout you want. I think some cool sconces on either side of a painting or some kind of wooden wall art above your fireplace could look really pretty. I would definitely introduce some color up there. If you want to get away from brown, you could add some cream colored furniture like this...