To discover new podcasts, I often search on https://www.listennotes.com/ for episodes about people or topics I find interesting.

I mainly listen to audio dramas. I find reddit the best place to get recs either that or I give advertised podcasts in ones I'm listening to a try.

I've been trying to get back into listening to podcasts over the past few years and something I've found is that the means of delivery is split. You can't rely on being available to subscribe to 'textbook definition' RSS based podcasts, it could also be on apple, spotify, youtube, an embedded player on their website, or any combination of those.

For me the best way was always personal recommendations from friends, sometimes also if a host of one show was a guest on another one.

I tried to build a better way to see what my friends are listening to with https://lastcast.fm, but I've since shut down the project.

Overcast is popular, but I would say its UI has also become worse over time:

https://overcast.fm/

But its less about discovery than tracking your library and playing them back.