I would really try to find a pice like your countertop - it will look so good it will be worth the effort. Talk to your installer.

Sadly my husband tried and the thinnest they can get is 3/4 inch which is too thick for our situation. Larger won't fit behind stove and sink gets too tight. Any 2nd choice idea?

Paint the back of the glass sheets the color of the wall? We are using backpainted glass sheets for our backsplash

You wouldn't even have to back paint it. It's glass, the paint will show through. Get a piece of tempered glass without the green tint and you will be all set.

I'd call these people to ask about whether glue shows through. Alternatively, clips or track?
https://www.dullesglassandmirror.com/glass-backsplash

Thanks. I wonder if there frosted would be less reflective. My husband does not want the shine. I will share this with them. Very helpful!