Hello Sdpg,
We see that you do not have the option to sync podcasts between your Mac and your iPod Shuffle. We'd like to provide you with a few details that may be able to help resolve this issue:
"If you have iPod classic, iPod nano, or iPod shuffle: You have to sync your device with your Mac. There’s no other way to add content to it.
If you have an iPhone, iPad, or iPod touch: You only need to sync with your Mac when you have new or updated content.
If you prefer not to sync your iPhone, iPad, or iPod touch, you don’t have to. You can download items from the iTunes Store, the App Store, Apple Books, and other Apple services directly to your devices. You can also use iCloud to keep items up to date across your devices."
Click here for more info: Intro to syncing your Mac and your devices
Best regards.