In February, we heard that YouTube Music would support podcasts, which now seems to be rolling out to users of the service. The interface in the app does not seem to have changed much compared to music listening, except that users can now fast-forward or rewind between 10 and 30 seconds, which can be useful when listening to podcasts. It is also possible to add both music and podcasts to your playback queue, just like in Spotify, for example.
Google has confirmed that the standalone app Google Podcasts will remain, but as usual with Google, it is unclear how much they can be trusted. Lately, the company has, for example, removed links to the app in search results, which makes one wonder how much Google cares about that app.
However, it does not yet seem that YouTube Music has all the podcasts that have been uploaded to an RSS feed, instead the focus is on episodes that have been uploaded to YouTube in one way or another.
The feature does not seem to have been rolled out to all users yet, but it seems to be only a matter of time before it happens.