First of all, it would help if you posted pics of your space.

Normally, sink faucet and pot filler match, in both style and finish. To my eye, to have them in such different finishes would look ”off”, as they tend to be near one another, and on almost the same plane.

Again, post some photos of your space, to give us a visual.

Match them

Match , better yet forget the pot filler

Unless you have a real use for that filler, I would nix it. They are really not done much anymore, and when they were considered fashionable, for 95% of remodelers, they were done just for looks. That said, if you are in the 5% who really, really needs one for some reason, all plumbing finishes should match IMHO. Good luck with your project!

The pot filler is already in and the backsplash is mosaic tiles. Not sure if I could remove it and have the splash look right? Thoughts?