new mac computer, old sansa clip, is there way to sync it with mac?

Is your Clip set to the USB mode of MSC? It must be in order to work with your mac. What mode was the player in when you transferred the music to it in the first place? If it was in MTP or Auto mode, your mac (or any computer) won’t be able to see it unless it is in the same mode. And macs don’t recognize MTP mode as it’s a Windows Media thing. Maybe that’s why your Music folder appears empty.

If this is the scenario, you will have to connect to a PC in MTP mode and copy the files back to a PC. Then disconnect, switch to MSC mode and transfer them back to the player. Now you should be able to connect to your mac and copy them over to that from the player, into iTunes.

And FYI, updating the firmware will not erase the music from the player. Only formatting does that.