Exactly what mjzee said. Dragging to music folders is actually not the easier method, because there are inner workings and extra steps that I won’t bore you with (and besides, there’s the easier method).
Also, are you wanting to use that external hard drive as your source … or are you wanting to transfer your external drive tunes to a newer drive - for example, your internal drive?
Seriously, just take a folder and drag and drop it in the left hand window and your Mac does the rest if you’re just transferring to your internal drive.
Again, it’s always a good thing to Google precisely what it is what you want to do: “How do I add tunes to Apple Music from an external drive?” and often you’ll get a link to an Apple forum or helpful magazine article with helpful folks if you have further questions. There you’ll find out what Migration Assistant and Time Machine are actually used for. Just hate to see you trying and trying other things that might not be the things you need in order to do what you want to do.