I have not done one. I only wonder how do you clean them? I wipe my tile backsplash of splatter all the time - that's why it's called a backsplash haha. I don't see how you can wipe brick, so I would think about that very carefully. Also, unless you have a lot of white in your kitchen, and a lot of light, a brick backsplash has the potential to make your kitchen dark.

As an aside, the photo with the gas range with the wood directly over it, and not much of a distance, gives me the willys. I know it's not what you asked about, but I had to mention.

I suggest taking a look at fireclay’s thin brick tile. Easier to install, easier to clean. Comes in a variety of colors

https://www.fireclaytile.com/gallery/category/brick/P12/

I don't suggest using real brick. It will be extremely hard to keep clean. But they do have brick look tiles that look pretty good these days.