You can use copper cleaner on both. It will remove the patina and make the metal very bright. It looks like toothpaste probably caused the bright spot in the sink and that's about the color you'll get once it's cleaned. The brass will be bright once it's polished. Both will darken as the patina returns but it won't be a nice even patina; it will likely look like it does now. You might be able to polish and coat with something to prevent darkening, if you want that look. If you want it dark with an even patina, that's probably going to be impossible unless you quit using it, let it darken naturally and evenly, then coat with something to prevent it from returning to the look it is now.

I love copper and brass, but avoided both for this exact reason. You could research if there are products which will add an even patina to brass and copper, then coat them to keep them looking like you want. This is for a kitchen sink but the rules apply: https://www.bhg.com/homekeeping/house-cleaning/tips/how-to-clean-a-copper-sink/

Try some white vinegar on the faucets. There is a dark finish on the copper that's failing. You will abrade it away to get it to consistently match. You'll keep polishing the copper or you'll learn to enjoy the funk.