You already have 4'' backsplash in granite. I would keep that way: simple!

But if you really want tile backsplash, I have two suggestions:

Your granite is quite busy so I think a subdued choice for the backsplash would be a good option. It looks very gold in the pictures. I think you could choose an offwhite or beige tile but quite plain.

Would you consider one of the options below in the hex pattern? Any of the 3 closest to the top might work but you'd need to see them next to your granite and cupboards. A tile like this still has lots of interest but doesn't compete with the busy pattern in the granite. Maybe even the black as it looks like black veining in your granite - but it might be too dark with your dark stained cupboards (which look beautiful by the way).

I know this one looks white but in fact the site says it is beige. It is hard to see but it has a crackle finish. Something like this in a different colour might work as well. Not completely plain but not competing. You could choose a contrasting grout as well and pull that colour from the granite.

Both tiles are from Saltillo Imports. It is located in Toronto Canada. Many of the HGTV designers source from this store and they have a wonderful selection.

Both of those options look busy between the granite and the stone overhead. Have you considered something that would blend into the background better? If you like texture, you could do one with texture but a more neutral color and in only one color rather than speckled like we're seeing. I think overall, simpler for the backsplash is better in this kitchen.

Choosing a backsplash can be overwhelming! Here is
a great article: A
Backsplash Guide

Stainless steel. Quilted sheet, or subway tiles.

Joe