The copy button should name its destination
A tiny confirmation is useful when copied text has nowhere visible to go.
I don't fully trust a button that says "Copied" and then leaves me alone with the original page.
Copied where? The clipboard, apparently. That is a real place, but it has no visible edge. I cannot glance at it to check whether the whole address went with the text, whether a line break got trimmed, or whether another application replaced it a second later.
The interface does not need to expose the clipboard. It could say what it did: "Copied link" or "Copied 12 words." For a code block, "Copied 18 lines" would be more useful than a green checkmark doing its little victory lap.
I would keep the button in the same spot and let the label settle back after a moment. The temporary message is fine. I just want it to describe the thing that moved, not announce that some invisible ceremony occurred.
A copy action is small enough to be boring. That is exactly why the confirmation should spend its one sentence well.