Thanks for posting here in the Google Nest Community.
This is not the experience that we wanted you to have, let me help you out. What is the exact message that you are getting from your Nest Mini when using this feature? What command are you using to play a podcast? Did you make some changes under Digital Wellbeing settings? Check some information below on how to play podcasts on your Nest Mini.
Use your voice to control podcasts and shows
Say "Ok Google" or "Hey Google," then:
Listen to a podcast:
"Listen to Oral History of The Office on Spotify"
"Play This American Life on Google Podcasts"
Listen to podcast by latest episode:
"Listen to the latest episode of Oral History of The Office"
Listen to the next or previous episode:
From the Google Home app:
Check this link for more information.
Hope this helps.