Such beautiful soft gray and teal in the tile. Keep that feeling. Your tile on my screen looks like this color. Very nice. It's called Sage from Glint at Home Depot ifyou're nterested. It looks darker on their site.

There is not much light in your photo, is the background Ivory or White in the tile?

Here's another gorgeous Sage green from BBBeyond if you like

I like it. I am not sure this shade you have is quite perfect but the saturation is delicious.

A dark complementary color is going to be harder to get right than simply matching the floor color exactly, but the payoff can be big.

I recommend getting large samples of potential paint candidates and propping them up vertically on your floor samples to be sure it's the right color.

👍