The iPod Shuffle does still work with iTunes, but you will need to use a data cable, not an audio one. It needs to be data at both ends.
Not only that, but if your MacBook is using macOS 13.6, as stated in your signature strip (although this isn't always correct), then surely it doesn't have iTunes on it? Instead, you use Finder to manage the iPod. (iTunes is still used on macOS Mojave {10:14} or earlier. From macOS Catalina {10:15}, it's Finder.
To return to the cable issue; presumably you have a charging cable for the iPod. That is a USB connector on one end and the iPod's 30-pin dock connector on the other.