Matte

My rule is that the backsplash must match one important color in the counter material, and I prefer the same finish (honed for both or polished for both). I don’t mix patterns in a small room like a bathroom.

Matte. Plus, it will camouflage water spots that ... splash back.

How high is the backsplash? the tiles look so basic. I think that using the stone on the backsplash as the counter would look best.

Use the standard 4” stone splash. You don’t need any extra details behind a bathroom sink.

I agree that the countertop material should be used as the backsplash. You can make it the standard 4" or go higher if you want. He put a 6" splash on ours.

the matte finish

I don’t think the tile goes with the granite and I would just use the granite.The Tivoli for sure does not work.

I wouldn't risk choosing a tile color that's close but no cigar to the shower tile. Use a ceramic tile in an off-white as close as you can get to the granite. Unless you're tiling the entire wall behind a vanity as a feature wall, you want the backsplash to blend in with the granite.

Thanks to everyone for their input. I did not go with the granite splash as the granite is 3cm-1.25" and was just way too heavy and clunky for a splash. I also noticed that photo I posted of the Tivoli tile is way too brown. The Tivoli is actually a creamy taupe color and our granite has a lot of taupe in it. Here is a photo

of the Urban Putty on the Tivoli tile. Back to the drawing board!