To migrate all your podcast subscriptions from Google Podcasts to the YouTube Music app, follow the instructions in this help document instead.
You can listen to private podcasts using the YouTube Music app by subscribing to the RSS feed directly. Private feeds do not appear in search results and need to be subscribed using the podcast's RSS feed link.
Start by copying the RSS feed URL for your podcast.
Click + next to "YouTube Music" in the subscribe link sent to you by the podcast creator. This was likely emailed to you with a subject line starting with "Your audio access:" Search for that in your inbox.
Then "Click here to copy the RSS feed".
If you can't find the email or link, contact the creator of the feed.
Visit the Podcasts section of the YouTube Music app here https://music.youtube.com/library/podcasts, or click the link to YouTube Music in the subscribe page.
Click "+ Add Podcast" (see below)
Click "Add a podcast by RSS feed" at the bottom.
Paste the RSS feed link that you copied above and click "Add".
Other apps have a one-click subscribe option that simplifies these steps. We are waiting for Google to create a similar option in their YouTube Music app. Until then, the above steps are required.