When I try to sync my iPhone using Catalina, the iPhone does not show up in the sidebar of the Finder window,

In Finder>Preferences is the iOS Devices box ticked?

If not please tick it. Then, with your device connected, click it in the finder window and all will become much clearer (assuming it appears)

If it doesn't appear try booting into Safe Mode. Others have reported success by doing this

Hello, BillGS.

Thank you for using Apple Support Communities! I understand that you're unable to sync your iPhone with your Mac, which is running macOS Catalina.

First, try the steps listed in the first two sections of the following support article: If your computer doesn't recognize your iPhone, iPad, or iPod - Apple Support

If you receive an error message, follow the steps listed here: If you see an error in Finder or iTunes on your computer - Apple Support

I hope this helps! Take care.