Try a mid-century modern rug like Hemphill's Rex Ray Area Rug Collection or Jaipur Traverse Caracas. I looked up 'mid-century modern rug' and chanced upon these on Houzz. I like the muted colours which would soften the cream on brown. The mid-century motifs would highlight the mid-century chair. Good luck!

I have a similar family room, with big windows and a sliding door and we have block out Roman blinds on them. They sit at the top of the windows most of the time as we don't have any privacy issues with being looked in at by the neighbours. We really only put them down at night in the winter. Ours have a creamy coloured background with taupy wavy lines on them. Very neutral. I never could have imagined that's what I wanted til I saw the fabric. Good luck I'll see if I can find a photo to post.

Suggestions from neutral colours: https://www.dulux.com.au/colour/colour-trends/2018/essential Ceiling & walls the same colour is a good choice for square set. There will be subtle hue difference in various lighting situations anyway, which provides depth and makes for an interesting look.

Can’t go wrong with natural white or snowy mountain 1/4 for a slightly warmer white with your tiles. Keep to warm colours. You floor looks warm but neutral and earthy, But then again photos on a screen can look different.