On Catalina, I have a station set up to show unplayed podcasts. Right now it shows a podcast from yesterday "Science Friday Part 2", but not "Science Friday Part 1", which I had to find by looking in "episodes".
It also doesn't show several other podcasts which I found in "Recently Updated", but which I haven't listened to (I'm tracking which episodes I listen to).
I have given up trying to listen to podcasts on my phone and watch because they won't synchronize with my Mac.
Best Answer
I personally also gave up on podcasts on the Mac. Maybe someone has a great app, but for me using Overcast made my phone / watch always with me and “perfect for this job” so my Mac can take a rest from podcast duties and only need to work when I listen to music and find it’s better than HomePod / watch / phone / iPad.
I know this doesn’t directly answer your question, but really - consider not solving this at all on the Mac is my advice. That way you don’t have to learn or even launch the current podcast app on Catalina. My guess is by August, we’ll know how many developers are making an iPad/Mac size screen podcast app and have another app to add here rather than use Apple’s native app.