If you always remain on AC power during the copy and your above Energy Saver settings are indeed accurate, then I can think of no reason why your system would enter idle sleep unless there is some process that specifically forces a sleep at some point. You can check for sleep entry & causes by examining the power management log:
$ pmset -g log
In any case, in order to prevent the system from going to sleep you can acquire a power management assertion with the use of
caffeinate(8), which is built in to macOS and accessible via Terminal:
The system will not sleep until you exit (via Control + C).
From your description, I suspect that you might not actually be on AC power the whole time and instead are running off the battery. Please double check this first.