The podcast section of Play Music does share many similarities with the overall Play Music app in terms of its cards layout, orange hues, alongside a strong focus on the cover art itself with small expandable descriptions. It has been divided into a couple of tabs – one for featured shows, and the other for your subscriptions, accompanied by a search bar at the top.
The search function remains universal across all of Play Music at the moment, so one should be able to get a better grasp of details such as songs, albums, artists, playlists, and videos right before you even see the podcasts within the results list. Since this change is one from the server side of things, it all boils down to your luck as to whether you can see it in the Play Music app. As long as you have version 6.3 and above, you’re good to go.