A possible work around:
You can access the downloaded podcasts from the Podcast app in a Finder folder, and then copy the files to another folder or device.
- Open Finder
- Open the "Go" drop down menu and press "option".
- You'll see a new entry named "Library". Open it.
- Open Group Containers
- Open the folder which ends in .groups.com.apple.podcasts There will be a group of alpha numeric characters before this ending.
- Open "Library"
- Open "Cache"
This "Cache" folder is where the downloaded podcasts from the Podcast app are stored.
I've added this "Cache" folder to the side menu of Finder for easy access until this issue is fixed in a future Big Sur update.
The files won't have the proper name of the podcasts (it will just be an alpha numeric string of characters), but they will have the dates they were downloaded. Therefore, you many want to rename the files so you can remember what they are.
I've been advised that the files should be copy and pasted to another folder and then deleted from the folder. Apparently it is not recommended that you drag and drop.
Good luck!