Long time ago, I used gPodder to download audio files with podcasts and then synced them to a mp3 player or mobile phone.

Nowadays I'm using gPodder on a phone with Sailfish OS:

https://openrepos.net/content/keeperofthekeys/gpodder

The app is actually linked from the submitted page, but it's easy to miss there.

I also noticed that if I create list of shows to listen to later, I end up listening to more interesting stuff, as I filter out items which are not as useful few weeks later.