Do you have spare tile to do a grout sample board and hold it up against your backsplash? I did a much larger black hexagon on my fireplace, and chose to go with charcoal grout, the shape would have been too much with contrast. But it was a completely different situation than yours. I would keep the grout on the darker side no matter what, definitely not white.

I don’t like to see a lot of contrast. I like how it looks now. I would go dark with the grout. Definitely agree on doing a sample board

Mapei brand Bahama beige / mahogany / or truffle. Bahamas beige is the one I’d do.

Will you be continuing this backsplash around the other areas, we assume? Go with a lighter grout (not white) and do not be afraid of the subtle highlights to the shape of the tile. You need it in your space for balance and dimension. Otherwise it is white, black, white with no transition.

I would go with a shade of grey that looks good with the tile if you do not want to go with charcoal. Black would be too dark and white, too light!

I agree that in this case you need to go lighter. You picked a hex tile to see the hex!

I definitely would take the time to do sample boards. You want to get this right.