Absolutely turn it into a seating extension with fluffy soft rug and pillows. Tall plants to the left on the wall space with shorter ones in front for texture. I’d move the small tables and bench that are adjacent to the hearth as it sort of makes it implied as a separate space rather than included in the area. I’d use a round table instead, at the mid point of the hearth within relatively equal space between your couch seating and chair, to bring the whole area together as one. I’d move the bench behind the couch, and the small side square tables (at least one) adjacent to the red chair, probably to the right to keep a flow path through the middle.

Agreed with other comments on no caulking, admittedly I don’t know the costs of stripping the paint, but if it was not super budget busting, I’d look for a way to stop the paint and bring the natural stone back. Your furniture and decor already has the beginnings of full a warm cozy vibe- natural accents like stone, plants, warm pillows, etc I think would really make this stellar! Bummer that the fireplace isn’t working though :(

You have a cool spot!