Kinda confusing question haha But let's say I have a new artifact and I use more Nth metal than the required for the milstone. Does the "wasted" XP get carried to the next rank? Or is it simply lost?
The only exception to XP overflow is Ally Favor. Ally Favor does not carry over, so always make sure you're loading up the exact amount needed. Everything else (OP items, augments, artifacts), you can just dump stuff if you so choose. Although, sometimes it's best to go slow so you can fish for crits.
Except if you're going for the max level of 200 you'll want to go slow. Because I do think you will lose any XP that's more than the amount you need for it to do the final breakthrough.
Well, technically you don't. But since there is no level 220 artifact currently (most likely not in the future either), there is no reason to overfill it.