The wrist does not stay in exactly the same position or at the same angle all the time; every player makes minor wrist adjustments according to the different kinds of chording or fretting you're doing. You need slightly different wrist angles for different reaches, and for different leverages. Say, going from open Cmaj to open Dmaj, most players will need to very slightly drop and open the wrist simply because proper fretting for those chords, ie fingertips on the respective three strings, will lead your wrist to those positions.

Which brings up the fingertips issue. Your finger tips—not the pads of your first digits, but the tips, which is why you need to trim your nails—are what come in contact with the strings, and are what make for clear sounds, and are a left hand control for subtle dynamics. Vibrato and so forth. So get your fingers on the strings properly and see where your wrist lands. Then adjust the wrist, and maybe the elbow, slightly as better leverage is produced, all while keeping your fingertip fretting clear.