This is all being done backwards. Paint and backsplash should be done AFTER everything else like cabinets painted. IMO the travertine was not a smart pick for a backsplash given everything else in the space. There's not "cooling it down". It's a warm stone that has pink undertones, no grout color is going to change that.

I don't think the coolr dark grey paint and countertop really go with it, but at least the warm wood cabinets relate to the travertine and trim. I'd hesitate to paint them white. If you're sticking with the travertine pick a warm grout to compliment it. I suggest changing the paint to something warmer, like a greige rather than that dark charcoal.

I'm not a pro, and I usually don't like travertine backsplashes, but my first reaction to your photos was that it was a lovely choice in your home. To my eye, the paint is complementary to the travertine and your wood cabinets & trim.

I do agree with Sina that your oak cabinets complement the warm tones of the travertine, and painting them would interrupt that continuity. I also would pick a warm grout that blends in with the travertine rather than stands out.