YouTube Music could become your new one-stop shop for listening to podcasts. If you live in the United States, you should be able to listen to them in the app or on your computer.
At the top of the screen, you’ll notice a Podcasts chip, as well as the rest of your moods such as Energise, Workout, Relax, and so on. When you click that button, you’ll be taken to a page with a list of the podcasts you’ve already watched/listened to. This list will also include shows you listened to on YouTube.