At least the slate-like tiles have a rough edge, more authentic? Would the vanity top make the tile look less, by comparison? Do you like transitional / informal...

No, the tiles are not rustic/rough edged or authenticate. They are mass produced, Home Depot-ish low grade in my opinion. We prefer traditional/transitional style...whites, grays, etc.

Did you have paint color thoughts?

To talk tile once more - yes, I bought that type at HDepot, but I meant it's not the cheapest tile at least. :)

You might have something with muted, grey-green paint... but less green.

Clark says MINDFUL GRAY "balances out other warm colors in a space; brown-tone flooring. Mindful Gray is a smart tool to counter those tones.” The designer recommends balancing it with both sides of the warm-cool spectrum for the best look.

Maybe this houzz quote suggests a gray not too cool, or too warm: "select a trim color - if painting walls a cool color (greens, blues, purples or grays), find a white that reads cooler. Put swatches of white paints next to one another and see how they compare; some will appear more warm or beige-like, and others very light gray with hints of green, blue or purple."

That's a tough call. If you try to blend with the floor then won't that be at odds with the vanity top?

Get a rug for in front of the vantiy and don't worry about the floor color. Match the vanity wood to the walls (white).

Add a framed print to the wall to draw attention from the floors.