Such as?

Just thinking about cleaning sauce and or grease spatter on a porus irregular surface like brick would not sdsit well with me. There is not a non pourous or smooth surface brick that I am familar with. I would just use a plain white subway tile everywhere.

The porous surface concern is real, but thin brick veneer tile solves most of it. These are genuine clay brick sliced to about 1/2" thick and mounted on mesh backing -- they look identical to structural brick, install like large-format tile, and take a penetrating sealer that makes them practical behind a stove. Old Mill Brick, Z-Brick, and Eldorado Stone all make interior-grade versions. The grout joints are much tighter than structural brick, which helps with the cleaning problem considerably.

For the stove area, running the brick there too and applying a food-safe penetrating sealer (Miracle Sealants 511 or similar) annually is one option. The other is a contrasting panel that reads as traditional rather than contemporary. Handmade subway tile in an off-white or cream glaze, slightly irregular in surface texture, echoes the brick pattern without competing and wipes clean easily. A 3x6 or 3x9 in running bond keeps it in the same visual language as the brick field. Honed limestone in a warm gray or cream would also work well against barley maple -- it needs annual sealing but handles splatter better than brick and gives you a single clean field at the stove rather than two different masonry materials fighting for attention.

The glass-covered-photo idea is worth setting aside. It reads in a different visual register than aged brick, and almost always ends up looking more contemporary than intended. If you want a focal point at the stove that feels period-appropriate, hammered copper or a patinated tin ceiling tile in a simple field can work -- they have more material kinship with brick than printed glass does.

One practical note: whatever you use at the stove, run it to the same height as the brick on either side. The range hood handles the visual interruption -- you don't need a height transition on top of a material transition.

You could use a sheet of stainless steel or copper behind teh stove.

A coat of semi gloss white paint is applied and wiped off some of the finish should protect the surface.

A few folks on here have brick backsplashes so hopefully they will weigh in - i would get it if I wanted it :) — it’s an easy change down the road if you use a thin veneer product

A stainless panel behind the stove would work - there are also brass panels on Etsy that look pretty great (wonder about floating glass in front of the brick behind the range? for an uninterrupted look but easier clean)

I love it when responders say ’if that is the look you want, here are some good ways to achieve it, and here are some other ideas to consider also’ rather than just NO.

i'd skip the brick backsplash ..not because brick is a negative for a splash ..... but barley maple would be a lot more interesting with something else. the busy brick will just dominate ...why dont you put in a slate floor or something there thats got the bit more rustic vibe.

an earthy green tile backsplash ...... more simple....no switching above the stove needed .....all together more complementary

Mandy Moore: Green Tile Backsplash for Jack & Jill Bath · More Info

Such as?

Linoleum.

Forbo is one brand.

https://www.forbo.com/flooring/en-us/market-applications/furniture-linoleum/pr93ex

I purchased a house with a very Tuscan kitchen that has tumbled limestone tiles for the backsplash. This is a second home, so I don't do as much heavy cooking or as frequently, but it does see a far amount on the weekends. I find it very hard to clean and anything oil instantly seeps in. Here is a photo of it with the brown grout, which did hide crud well, but I got tired of the heavy Tuscan look and painted it off white this spring. The white has lightend the look, but oil still seeps in. I am now going to try putting a matte sealer over it to try to give it some more protection. I would not voluntarily put something so porous and unwipeable in as a backsplash. Have you considered perhaps beadboard?