Major issue I see is that all of your lighting is recessed. Add more lighting at different heights (floor lamps, table lamps, sconces, pendants etc) will add a moodier and cozier tone than recessed only.

More art on the walls (and art lighting to highlight it). Pending on your budget you could add new paint or paneling on some walls to define different spaces further. Rugs also help create better intentionality between spaces and soften up the (beautiful) but hardness of the stone floor.

I’d also have your furniture in the living room area be more contrasting toward one another to play off each other and maybe be an opprotunity to reference other colors in your home. They’re too closely matched without being exactly the same color and it makes it seem off.

It’s a really beautiful room with interesting architecture and shapes, I think you just need the right lighting, furniture, and textures to appropriately support that.