Sage green would be nice with your cabinets, if they’re green which is the way they appear on my monitor

It looks like you already have a backsplash. Are you just looking for something to go behind the stove?

I wouldn't put tile above the counter ledge, what about a clean stainless steel panel behind the range?

Yes, behind the stove or open to everywhere. I just don’t love the look of a stainless steel panel!

The 4" countertop piece of quartz is your backsplash - if you want tile, you should remove the piece of quartz first.

Also, I agree with Diana above - the cabinets look like a grayish green. I wouldn't use a blue tile.

I love Fireclay tile in "Rosemary"

If no stainless, then I’d just do a panel of glass behind the range for easy cleaning if it were me

Do you have any local independent tile stores in your area? They have large grouted sample boards that make it much easier to select the right tile. They usually let you borrow a few boards for 2-3 days.

A light tile in the background color of your quartz would look good. I wouldn't pick a tile with high variation (V3 or V4) because you already have variation in your counters.

Make sure to remove the quartz backsplash strip if you decide to tile the whole area.