So I purchased another one of these, and my first Magic-NS might be an earlier model, because only the 2nd one I purchased came with a USB C cable. Only the box of the 2nd one I purchased says that it comes with one. My first Magic-NS would only function if I turn on the Switch while the Magic-NS is unplugged, but the 2nd one doesn't have this issue.
Sounds like some kind of glitch or bug if you ask me because I bought one early without any cable and it's constantly left in the dock without problems.