How to make those large square tiles look more modern

I'd try stenciling a design on them. Practice on paper after you've found a design you like and use craft paint specifically for tile and glass. Maybe just a focal point over the sink or stove.

for the backsplash try to find some cool looking window clings. Are they all the same color? same texture? All neutral? You could find some more colorful accessories that would brighten without even having to alter any tiles. Go crazy with like dark red or purple, if the tile is dark, so all white to make it stand out. Easy to bleach white things!

Use Stick on tiles or Sticky back tiles or Trasphers or Use Decoupage or Fabric and Mod Podge to make a difference. Or Stick on Smaller tiles in centres etc........