Instead of click-to-copy, you could do click-to-highlight, so that "right-click > Copy" highlights the text on right-click if it's not initially selected. There is some subtlety in the logic, because it shouldn't interfere when the user manually selects a substring.
I'm aware of that gesture, but I think it shows the point that it requires extra intention from the user to do select+copy on an input-looking field with copy button attached, instead of being part if the default ctc button experience.
Not that I am searching, but I wonder if there's already tog/nielson/other ux research on this specific interaction.