I would do gray walls and just make sure it has the same undertone as the tile I often paint the ceiling the same as the walls if going with a light color or if a little darker for walls I cut wall color 50% for the ceiling. I have a gray and mostly white LR and I have walls a color called Vancouver Day from C2 I then add color for different times of the year with pillows and a few accessories The wall behind the sofas I just painted in a purple from one of the pieces of art and I love it.

I feel partitions are not needed. You already have too much for the space. Adding a partition will shrink the space further. The simplistic solution, you do not wish to discard any furniture would be to paint all the walls in lighter pastles. And use some wall painting frames to highlight certain walls.

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