The OP is saying that the older versions of the Podcasts app was much better than the current one, in respect to saving podcast episodes. Sometimes, episodes are removed, so you can't listen to them again unless you've saved them somewhere.
You used to be able to download the episode, then simply drag it onto your desktop. This copied it from the cache folder in the library, leaving it available to play both through the Podcasts app and separately.
I used to do this a LOT. It was easy.
Now, you have to open:
/Users/darkpaw/Library/Group\ Containers/<random_chars>.groups.com.apple.podcasts/Library/Cache
and manually figure out which file is the episode you're looking for. You just see a list of UUIDs. Some of the files will have an icon, but that just shows the podcast, not the specific episode.
It's a fresh hell that Apple didn't need to create.
I've decided the way forward is to delete a download via the Podcasts app, open the cache folder, then download the specific episode again. It's manual and annoying, but the latest file will be the one you're looking for.
To the OP, send some feedback to Apple. At the very least they should restore drag & drop functionality.