I just completed a high-end kitchen remodeling, not a 500k job but a 150k job, give or take. The fabricator book-matched the countertop with the backsplash and waterfall perfectly.

Not sure what vein pattern your slabs had, but when joining two or more slabs, it must be done in a way that they mirror each other. On larger jobs, when using multiple slabs, the vein pattern must continue from one piece to another, and the pattern must continue across multiple slabs so they can be matched.

Good luck

You have the 3cm of the covered counter to have the pattern be off. And without buying at least 4 slabs for the counter and backsplash, the expectations should be tempered as to what is physically possible with bookmatched natural stone. You can get "flow" without a "match" with limited material. If "match" is highly important, that requires more material on the front end.

Quartz is both easier and harder to match the vein flow than natural stone. Stone with a large unified background, with directional veining, is easier. Quartz with more veining, and either bolder or more subtle, is harder. And quarts WILL SCORCH when used as the splash behind a cooking zone. All the pros know this, even if they want to ignore it and pretend they don't so they can act surprised and blame it on the stone fabricator.

lower your expectations. It's not going to match exactly.

What is the alternative? If you want the backsplash the same material, let the professionals do their job. No doubt, it isn't their first rodeo.

You need to find a fabricator that has pride in his work and also has artistic/design abilities to produce perfectly lined up "works of art". Most fabricators have neither of those!

The fabricator we used in CA, referred by a designer friend. He created curves and layers out of flat 2 cm stone slabs ...