im going to give and answer and shill for portable apps for windows users. way easier to migrate machines when you just need to copy over a directory. https://portableapps.com/apps/internet/gpodder_portable

Just out of curiosity, what’s wrong with podcasts on the phone?

I’ve been using Podverse but I’m not sure if it meets your requirements. I just use it in the browser when I’m on Windows. The Android app doesn’t seem like a web wrapper. Its source code is available under the AGPL. I’ve been paying $18 per year for the hosted service, but they provide instructions on self hosting.