Your old hard drive is attached to an SATA connector, which is that external cable, correct? Yes
And that cable then plugs in to a USB port on your "new" iMac. (still correct?) Yes
What happens now when you plug in your OLD hard drive? How does THAT show up in your Disk Utility now, and how does it appear in the other System Information screens that you posted already with only the internal drive showing? See attached
And that cable then plugs in to a USB port on your "new" iMac. (still correct?) Yes
What happens now when you plug in your OLD hard drive? How does THAT show up in your Disk Utility now, and how does it appear in the other System Information screens that you posted already with only the internal drive showing? See attached