Currently Mac-app-based: Downie, set to create both mp3 and mp4, with Hazel sweeping mp3s into Castro’s sideloads folder. Downie has been a nice break from the instability of the whole youtube-dl/yt-dlp situation. I used to use huffduffer and the converter a lot and would happily go back if my situation changed.
I assume you are listening to podcasts that are not on a podcast app and are only on YouTube? I just lock my screen, and YouTube keeps playing in the background, but that may be the case because I use YouTube premium