Those cabinets are transitional, as you say. So take the backsplash bright and modern, to pull them into the modern look. I'd go with white glass tiles. Snow white gives off a very pale blue undertone, which will go nicely with your paint color.
Put in LED under cabinet lighting (inexpensive and easy to install) which will add brightness to your countertops.
Change your drawer pulls into more modern straight handles .
If you want to add color, try different pendants. These come in a variety of colors.
Good luck!
Q
Very talented
Q