US YouTube Music rolling out podcast support
YouTube is now offering podcasts on YouTube Music in the US! Don’t worry if you don’t see it yet, they’re gradually rolling it out with reviewers and people who write about it solidly back of the line ;)

You can enjoy podcasts on-demand, offline, in the background, while casting, and seamlessly switch between audio-video versions.
You can read more about the release here.
If you want to know how to find podcasts in YouTube Music, here’s your guide.