How do I see unplayed podcasts?

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.

• https://overcast.fm/

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.