My ipod shuffle would not show up in the finder when I plugged it in. Here's a workaround that worked for me:
Open Music App
Click on your iPod shuffle in the sidebar
You should see a Sync Settings button in the upper right
That will open the finder window where you can sync podcasts
From what I found there is no way to add an audio file into Podcast application: as of macOS Catalina, it supports only subscribing to RSS feeds. The only way built-in way to listen to the separate podcast episode is to find it via application search and add it separately.
However, I found out that you can listen to any audio files including MP3 the same ...