Unable to download music files to external hard drive on my Mac Pro

I plugged in my external hard drive to my Mac Pro, hoping to download new music files, only for a pop-up for Finder asking me for my Apple password before allowing me to do that. I put my password in several times. It keeps saying it’s wrong. It’s not. I’m finding this very frustrating. Never happened to me before. Is it just me or since AI got released, are these computers getting more stupid instead of more smart?? Talk text is a nightmare these days and now this come on why is this get so hard? whatever happened to user friendly?

[Re-Titled by Moderator]

Original Title: Downloading files to my external hard drive