Could you try a different network connection / cellular data to see if the issue would persist? It's worth logging in to a different account, if possible (a friend's or a relative's would do) to check if you'd be able to play the podcasts there.
We appreciate the info! Could you also try what @Yordan has suggested to see if it makes any difference? Creating a new account for testing purposes may be a good alternative here as well.
Hey folks,
Thanks for your patience while we looked into this issue.
We’re happy to announce that this should now be fixed for everyone - just make sure you're running the latest version of Spotify.
If you're still having trouble you can post a new thread in the relevant help board here.
Have a good one!